1799-1812.
After the First Global War, a new world order has emerged, a very uncertain one. Spain was devastated and lost much of its empire, Britain was humbled and lost numerous possessions, Russian expansion was continuously frustrated in the west and France seemingly ruled supreme, but was still surrounded by enemies and mistrusted. Apart from that, Scandinavia suddenly emerged (or reemerged) as a great power, Prussia still dominated Germany east of Rhine and north of Austria but was quite discredited by recent defeats, Austria was hemmed in between not-so-cordial allies and even less cordial enemies and the Ottoman Empire was unstable, yet resurgent in the face of Selim III's reforms. Outside of Europe, colonization of new lands continued and intensified, whilst the Western Hemisphere saw much strife. The early 19th century was to be that of change all over the world.
In North America, the four post-Presidential nations coexisted with much hostility and border skirmishes, but no major war between them came. The strife resulted in the emergence of two alliances, along cultural lines - the "English Alliance" (a reconciled DRA and NEF, united by their fear of the Francophone powers; this alliance also was increasingly friendly with the British) and the same old Francophone Entente (Canada and Louisiana, which solved a border crisis by drawing a horizontal line west from Mississippi River's northernmost point; territories south were to go to Louisiana, territories north were to go to Canada). All-out chaos in the Carribean was ended by a French intervention in 1806-1809; in spite of fierce resistance by the rebel slave forces, the French have (re)captured Puerto Rico, Haiti and Cuba. They used the newly-acquired base to intervene in Mexico, assisting liberal rebels against "Emperor Manuel I of Mexico". In spite of British protests, France and Louisiana soon enough won a total victory against Mexican government forces; "sister republics" in Sonora (north Mexico Proper), Mexico (south Mexico Proper), Yucatan (Yucatan) and Guatemala (all of Central America including Panama) were set up, and Lousiana annexed all Mexican territories north of the Sonoran Desert, expanding all the way to the Pacific Ocean; the new lands were sparsely-populated and rebellious, though. In response, Canada somewhat sped up its slow westwards expansion, mostly driven by fur trade until then. Russian expansion in the region was, however, nearly nonexistant as the Russians concentrated on other matters at the time.
In South America, it took many wars, rebellions and interventions for a semblance of stability to appear, or at least for vague boundries between new nations to appear. Francisco de Miranda played a large part in this - having led an early Venezuelan rebellion, he then made a bid for the unification of South America, but was defeated badly at Ibarra in 1806 by British-backed Peruvian troops (the conservative Peru immediately refused to acknowledge the Spanish Republic and rose up in arms, led by a Spanish soldier and nobleman, Ramon Odria, who was declared "regent of the Peruvian Empire"). With French "assistance", he was persuaded to ally with the Spanish Republic, in exchange for becoming the ruler of an "Autonomous Republic of New Granada", but this only ignited a bitter civil war within the former Vice-Royalty, and Peruvian Imperial troops, augmented by the auxillary "llanero" cavalry, quickly advanced to Bogota. The eventual peace treaty left the Peruvian Empire in control of roughly the southwestern half of the ARNG, with the rest becoming a rather less autonomous part of Spain, though occupied by France. To counter-balance the growing French influence, however, Britain has formally allied with Peru, and assisted it in taking over the chaotic Capitancy-General of Chile and in consolidating rule of the southeastern part of Peru itself (namely, Charcas, which is approximately OTL Bolivia; in OTL it was shifted to the Provinces de la Plata, but due to British control of Buenos Aires, that Vice-Royalty is much weaker and smaller then in OTL). The British intervention, in spite of French protests, also helped the Portuguese crown maintain hold on all of Brazil - the north was pro-Portuguese anyway, and the south was hemmed in between Buenos Aires and Rio de Janeiro. All-out chaos in the remnants of Provinces de la Plata and need for a land supply route to southwestern Brazil (the comparatively recently-acquired regions east of Parana) allowed and caused, respectively, the establishment of a British protectorate, as the conservatives in the country gladly declared George IV (George III died soon after the defeat in the FGW) their king. As time went, the Platine Protectorate evolved into a "dominion" (which is less auotnomous then in OTL, but more autonomous then a protectorate). The French looked on with dismay as the British influence in South America grew tenfold, but were unable to do more then what they did (moral and slight financial support for the rebels) due to other concerns.
Most of said concerns were in Europe. Britain itself, after the defeat, begun quickly strenghthening itself. The Industrial Revolution was given additional impetus by the great damage done to the British commerce during the war. It was quickly reestablished, but if revenge was to be achieved, Britain needed to be more self-sufficient. And industrialization was an important element in the internal development that, the Parliament concluded, was neccessary. Lafayette may not have come to similar conclusions, but regardless, he didn't matter much after 1806, when he, tired of intrigue and of the burden of reign, exhausted by the mounting conspiracies against him, and perhaps blackmailed by certain persons, resigned. But he didn't declare any "successor" - he, instead, declared the formation of a real republic. A Montesquieuan democracy was to be established. Electinos were held, and the war hero Napoleon Bonaparte won. But the early instability doomed the "democratic republic" - Charles-Philippe (who wanted to become Charles X) decided to stage a coup d'etat, using the conservative sentiments in the countryside. Arriving from Britain by ship, he landed at Saint-Nazaire, and started the "Royalist War". Vendee immediately rose up in arms against Bonaparte, and rebellion spread fast. Peasants took up arms, and urban conservatives were only waiting for Napoleon's grip to loosen... which it, however, didn't. The Corsican wasn't about to let go of the power. He declared martial law, and weeks after the First Consul lost dictatorial powers the new one has regained them all, the Assemblee being either Bonapartist, either non-Bonapartist but still afraid of Charles-Philippe, either too busy defecting to the Royalists.
Napoleon Bonaparte's organizing skills proved crucial in the first two months of the Royalist War. He picked the right people for the job, leaving only the grand strategy for himself, at first anyway. Lazare Carnot organized a mobilization of the French population, Georges Couthon terrorized the conservatives into submission in the north, where he was still in position to do so, Marechals Lazar Hoche and Andre Massena marched to Rhineland and Italy respectively, whilst Admiral Georges Flandin established a blockade of Vendee and prepared the fleet for a clash with the British (those military measures were, ofcourse, undertaken to make sure that the Holy Alliance didn't intervenne). And meanwhile, Marechal Victor Moreau marched to clash with Charles X... but things went wrong there. Harrased by the Royalists who didn't want to give battle yet, Moreau advanced towards Nantes, and there he was allowed into the city, then attacked from inside and outside. The situation might have been salvaged, but Victor was hit by a stray bullet and thus a rather small part of his army managed to escape. Thankfully, his army wasn't very large when compared to the ones about to be ready, only 20,000 men, but those were good, experienced men, and even if the defeat itself was quite reversable, the psyschological effect wasn't, or at least not as easily. Rebellions spread. Napoleon Bonaparte had to take personal command.
And that he did, with results. In early 1807, or more specifically in the 27th of January, the Royalists suffered a decisive defeat at Le Mans, and Charles X's triumphant "march to Paris" was cut short. Rebellions in the south of France were cracked down upon quickly. After another defeat at Loir, the battered Royalist army disintegrated. What came afterwards was a grueling guerrila war, but the worst was over. Eventually, Charles X was caught and guillotined, and the Royalist partisans were tracked down and exterminated. Vendee was badly depopulated by the fighting, the reprisals (by both sides) and by the following "exodus" to Britain of Royalist sympathisers afraid of the victorious Republicans. The rest of France wasn't hit as badly, but things were unpleasant.
Italy and Rhineland were increasingly hard to maintain due to the growth of Italian and German nationalism respectively. The rise of Napoleon, a Corsican and thus related to Italians, to power in France has resulted in a slight improvement of this situation, but it nonetheless was a menace, especially as Austrians begun courting the more conservative and/or pragmatic of the Italian nationalists...
...and indeed, whilst Lafayette faced fairly incompetent enemies, Napoleon had to face a whole new generation of Holy Alliance leaders. In Britain, as mentioned before, George III was replaced by his son, whilst the new Prime Minister was Richard Sheridan, who was determined to avenge the defeat of the FGW no matter what, being rather embittred by the French invasion of Britain, during which he lost his son. In Prussia, Fredrich Wilhelm III (who is quite different from OTL, due to a much different Prussian history) was just as determined to right the wrongs of 1799. In Austria, Leopold III made some concessions to liberalism and parliamentarism, but kept power in his hands through capable intrigue; he also had far-reaching plans for extension of influence in Italy and the Balkans. An interesting situation developed in Russia (as far as France was concerned) - Empress Maria I (who came to power after the five month reign of Pavel I), though definitely a political genius and not too predisposed towards France, was much more interested in internal development and Asian expansion, whilst paying lip service to the anti-French cause. Or perhaps it was all a ploy?
On the French side, apart from the sister republics, there were the Scandinavian Republic and the Ottoman Empire. The former was an odd one; created in the wake of the bloodless coup that got rid of the incompliant king, it was rather resemblant of pre-Patriot Netherlands, a mercantile-aristocratic "republic", though the poor were also represented. It still was rather weak, but it has been preparing for war this time, fortifying Helsingfors and Stralsund. As for the Ottoman Empire, some progress was actually done. The Janissaries, whom Selim suspected of treachery and hated for inefficiency shown in the previous wars, were executed to a man. The feudals were cracked down upon as well. The Sublime Porte was being revived, with lots of French help. For instance, French engineers were, as of 1812, hard at work on the Suez Canal, to link French and Dutch Indian Ocean possessions with Europe and to outmaneuver the rapidly-rebuilding British fleet. In the Middle East, an Egyptian rebellion (amongst its causes was the French presence in Suez) was put down, Hejjaz was reconquered and a bitter war with the Saudis was taking place. Finally, in 1809 the Saudis, battered by previous defeats at Karbala and at Medina, suddenly came under direct Turkish attack. A large Turkish army marched into Arabia and razed ad-Dir'iyah, the Saudi capital, to the ground. The Saudi family was slaughtered nearly to a man, and any towns of importance were occupied by Turkish troops. Most Arab tribes were won over by lavish gifts and adroit diplomacy, and the Wahhabi heresy was subject to a ruthless repression, being hunted down and exterminated by the Ottomans and their allies. The Wahhabis had nowhere to flee, and most of them either died in battle, either were reduced to small, sparse bands of nomads, although many crypto-Wahhabis remained.
Elsewhere in Africa, Moroccan support for anti-French rebellions in Algeria resulted in a temporary success of said rebellion... until the French got around to putting it out and to invading Morocco. Sultan Mawlay Sulayman died in battle, and thus Morocco was occupied and annexed by France, apart from some lands around Tangier that were taken by Spain and the port of Agadir, which was occupied by the British. That was one pre-war crisis more. France also expanded in Senegambia and grew its influence in Madagascar, whilst the Dutch settlers in Cape Colony dealt a decisive defeat on the Xhosas, extending Sudafrika north to the Orange River; the crippled Xhosa were finally destroyed as a force by Dingiswaya of Mtethwa, although not before inflicting heavy casualties (one of the dead was a promising young warrior, Shaka, whose heroic sacrifice saved the Mtethwa horde in the final battle at Thaba Nchu). Dingiswaya went off to found a tribal empire in the east of southmost Africa, which collapsed after his death. Scandinavia jumped in into the colonization, mostly for the sake of the prestige involved but also to get slave trade income, which the ruling mercantilist faction really wanted, no matter what the French said about slavery; Scandinavian trade outposts were established in Gustavia (OTL Liberia).
Empress Maria's Russia was determined to extend its influence in Central Asia, where expansion was feasable and comparatively easy. The annoying Kazakh raiders of the Middle Horde were put down by a series of expeditions in 1802-1806; the unstable non-Ottoman Caucasian states, most notably in Aizerbadjan, were forced to acknowledge Russian protection, to the Ottoman outrage and dismay; war-wrecked Qajar Persia was provoked into a war by a Russian-backed Azeri rebellion (the Azeri elite decided that better Russia then Persia; taking into account the fact that Persia was increasingly anarchic, that wasn't an unreasonable choice considering that Russia was likely to come there anyway) and, with tacit British support, was reduced into a joint Anglo-Russian protectorate, also ceding Persian Aizerbadjan and the Caspian coast to Russia; and finally, Russia extended its caring protection and economic-poltiical domination to the Uzbek khanates, that were by then quite desperate due to the Turkmen raids. These conquests improved Russia's economic situation (as new markets were forcefully opened) and allowed Maria to crack down on those annoying nomad raiders and slavers.
Under Arthur Wellesley's brilliant leadership (he was appointed viceroy after his brother's death in 1809 (due to old wounds and bad health), continuing the "Wellesley Dynasty"), British power in India begun to recover in spite of the rise of the Sikhs and the Gurkhas; indeed, the latter were crushed and subjugated in 1811. Internal reforms in British Bengal and the disintegration of the Maratha Confederacy allowed the British to reclaim Central India in spite of a botched Mysorian intervention. Aside from that little accident, however, Mysore was still quite strong. A hybrid Hindu-Muslim culture (but not a Sikh one) was emerging, an alliance with Punjab was signed, and Turkish-style French-assisted reforms continued.
Indochina was in crisis, and disturbances spread, followed by reforms and (more or less) strenghthening of the three mainland states: Myanmar, Siam and Vietnam. Resources of Myanmar, under Bodawpaya, were pushed to their limits in wars with all neighbours, culminating, in 1801-1808, with a war against Britain and Siam. In spite of early successes in Assam and Arakan, in part due to French assistance, but eventually Rama I of Siam and Arthur Wellesley of British India defeated and captured him at Bassein. Arakan, Assam and Irrawaddy went to Britain, whereas Siam took over Tenasserim, Pegu, Shan, Chiengmai and Kayan - thus, Myanmar was reduced to a rump, land-locked state in the north. Back in Siam, Rama I (also known as Phraphutthayotfa Chulalok...) reformed with British help, turned the village of Bangkok into a great capital and expanded into Cambodia and Laos (disunited as it was). In Vietnam, the Tay Son rebellion, backed by the French who seeked to counter the pro-British Siam, resulted in the reunification of the country and in French-backed reforms. It also caused another event that will have repercussions later on - the Chinese invasion of Vietnam, back when the counter-revolution led by Nguyen Anh (who in OTL became Gia Long) seemed to be on the brink of success, was beaten back with French help, and the Chinese had accidentally learned of this. The war was over as soon as the invasion ended, as neither side bothered to push forward, but Franco-Chinese relations would suffer. The British, meanwhile, took note...
First serious French settlement in Australia was established in Lafayettesville (OTL Perth); colonization of Australia was generally slow, though the concentration of British loyalists in British Australia gave the British an edge.
The year of 1812 didn't see the Second Great War begin; neither with the year of 1813. But the road to war has already begun, and both sides were preparing for a showdown that will be even more global and even more bloody then the FGW...