As 1798 begun, Pichegru (who left Talleyrand, an ever closer collaborator, to virtually control the country's domestic affairs until his return, in collaboration with various ministers and Sieyes ofcourse), Cadoudal and Bernadotte led the rebuilt Army of the Rhine to finally crush Erzherzog Karl, whilst Augereau and Massena took charge of the likewise-strenghthened Army of Italy and set out to check the Austrian advance across the Alps. The armies, reinforced by conscripts and volunteers, were immense, and several roads were clogged by them and their supply wagons. The drum-beats and war-songs, including the Marseillaise despite the petitions to forbid it (that won out in the end, but only after this campaign was over), could be heard all over France, as new conscript companies were being sent to catch up with the armies. The morale was high; the soldiers, for the most part, were led by the generals they learned to love or at least respect, and though most of them, apart from Cadoudal's ragtag "Royal Guard", were not inspired by either revolutionary or reactionary zeal, that was wisely replaced by patriotism and nationalism, which quickly turned into France's ideology and was quite popular. Furthermore, Pichegru had promised "one last campaign to end the war"; a promise that quite popular in the war-weary nation. The people and the army just wanted this to be over with - over with a French victory, ofcourse. The French armies, as already implied, were very numerous; training and organization somewhat suffered, but morale and numbers made up for that. As for the supplies, there were enough for this year at least.
But France's greatest victories were not won on the battlefield, even though the most famous naturally took place there, and even though France's forces were, despite occasional setbacks, triumphant this year, gloriously so. The greatest victories were scored in the pockets of courtiers and officials, in the ears of monarchs and their advisors, and in decrees that shattered the Coalition and brought France out of diplomatic isolation.
Not that it was in diplomatic isolation. Already in 1796, Spain, for all the good it has done to France, had allied with the Directory; despite some dissent early in 1797, the Spanish government was elated to support Pichegru, despite his occasional radicalism, as the alliance with France was always first and foremost a pragmatic one; the Restoration of the monarchy, however, made it a dynastic one as well. However, Spain was a pretty useless ally, as the Battle of the Cape of St. Vincent had proved. Talleyrand needed some new ones. Some good ones.
His attempts to find allies in Sweden and Russia both failed, but already in December 1797 not only both officially recognized Pichegru's regime (they recognized Louis' coronation much earlier, ofcourse), but they also left the Coalition altogether. Neither power had any real interest in fighting the French; if anything, the Swedes were France's traditional allies, and intervenned in a mostly-token fashion only out of anti-republicanism. As for Russia, Pavel I, unlike his mother, didn't care about the revolution at all, he was eccentric and unconventional, and intended to make peace with the Republic in any case. Peace with the Monarchy was a must-have. Some fight wars for peace; Pavel I signed peace to free himself from all this west European nonsense and to resume the struggle with the Ottomans. Already in early 1799, as the war's last battles were being fought, the Russian forces crossed the Dniester in the support of Alexander Ypsilantis, who led a Graeco-Romanian rising in the Danubean Principalities. But more on all that later.
Talleyrand's search for allies continued. On March 12th 1798, a few days after the Prussian army's defeat at Kerpen, Friedrich Wilhelm III officially backed out of the Coalition and signed truce with France; a few days later, in what was dubbed the Second Diplomatic Revolution, Prussia signed the Treaty of Potsdam, not only confirming the Treaty of Basel that left the lands west of the Rhine in French hands, but also pledging to ally with France against Great Britain and Austria, accusing them of betraying their original war aims and seeking nothing but self-aggrandizement. The Prussian army in Rhineland, prevented from linking up with the Erzherzog by Bernadotte, now linked up with Bernadotte and went on to help Pichegru's main forces destroy the main Austrian army and capture the Erzherzog himself in the decisive Battle at Bonn. Meanwhile, despite Prussia not really being prepared for such a campaign, Gebhard Leberecht von Blucher steamrolled through Saxony, which was even less ready for it than Prussia. Taken aback by this betrayal, the Austrians marshalled their forces, and succesfully repulsed an attack on Prague, but were themselves defeated at Tetschen, thus failing to push Prussians out of Bohemia. Their forces on the Rhine were, ofcourse, also in shambles. In Italy, the Austrian army won a pyrrhic (and at that, incomplete) victory at Moncalieri, but failed to dislodge the Army of Italy from the more mountainous westernmost parts of Piedmont, much less Savoy. Austrian diplomats pleaded at the Russian court, but got little sympathy and nothing beside that. The German princes, realizing that they were hemmed in between Prussia and France with Austria unable to assist them in any way, immediately signed separate peace with France, even those of them who had lands west of the Rhine (they ofcourse had to sign these away in exchange for a meager compensation). Ofcourse, the derranged elector of Hannover, better known as the insane king of Great Britain, remained loyal to his Austrian allies, but he was little help, if only because Hannover itself was attacked by Franco-Prussian forces let through by the other German princes and overran without much of an effort.
The last few battles in Normandy (an utterly bungled last-moment British invasion), Italy (Austrians forced to fall back from Turin, although they managed to maintain an orderly retreat and later thwarted an invasion of the Duchy of Milan) and Bohemia (Prussians pushed out of there, but defeating an Austrian invasion of Silesia badly) weren't really important. Already in the end of 1798, the British, war-weary, dissent-racked, uncertain of their own aims and also, due to remaining dynastical influence in the system, threatened with the long-term loss of Hannover, begun probing for peace; in January 1799, just a year after the victory at Rivoli, the Austrians called for a truce as well, desperate and fearful that if the war goes on like this they might lose even more than it seemed they were about to lose now. They were also somewhat fearful that Russia might enter into the fray, and that the recent invasion of the Danubean Principalities was in fact merely a cunning flanking maneuver that exposed Transylvania to Russian soldiers. It was decided that the new world order was to be determined by a conference of the great combatant powers in Versailles, on the occassion of its restoration as royal residence (but not as capital; this was in fact seen by many as yet another sign that the king was being literally moved away from real power). Notably, nobody invited any Saxon or Sardinian delegates; only Prussian, Great British, French, Spanish and Austrian. They wrote up the peace treaty and imposed it on everybody else.
First and foremost, the Coalition recognized the previous Treaty of Basel, while France (and, surprisingly enough, Prussia) recognized - with some alterations (see below) - the Partitions of Poland. All sides agreed, after some bickering, not to pay out any reparations, apart from a minor Prussian financial compensation to Austria in exchange for the territorial changes. Speaking of the territorial changes, let us begin with the issue of colonies. Britain restored France's meager colonial empire, even French Guiana, but annexed the previously-Spanish Trinidad y Tobago. The Dutch colonial empire suffered most; though the British returned most of the Dutch East Indies, the Cape Colony, Dutch Guiana and Ceylon were annexed. In Netherlands themselves, after much debate, a federal republic ("Batavian Republic", later renamed and restructured a few times after some more coup d'etats, ultimately becoming the "Dutch Confederation") (undergoing - out of its own accord - "deunitarization" after the brief, unpopular dictatorship of the unitarian democrats) was retained and forced to pledge perpetual neutrality (in European issues, anyway). In exchange, all the signatories of the Treaty of Versailles guaranteed the independence, territorial integrity and neutrality of this Confederation. France was recognized in its possession of Austrian Netherlands, Limburg, Rhineland and Luxembourg in the north, while in the south, it annexed Savoy and Nice, but restored Piedmont to the Kingdom of Sardinia, which also got the Republic of Genoa in compensation and became the buffer state between France and Austria in Italy. Austria, in compensation for its numerous losses, annexed Venice, and formally retook the Duchies of Milan and Tuscany. Aside from all that, Italy was returned to the status quo of 1792, officially anyway. Major reshuffling occured in Germany. The Holy Roman Empire was retained, although it ofcourse lost the lands west of the Rhine, and even underwent some reform later on (basically becoming like a League of Nations, only in Germany). Prussia withdrew from Hannover, but annexed the meager remnants of Austrian Silesia and West Galicia (clarification - I mean the territory Austria annexed per the Third Partition of Poland, including Cracow and Lublin; NOT the west of the parts of Galicia that it ultimately retained), not to mention Saxony. The Wettins also lost Augsburg to Bavaria, which also gained Ansbach and Bayeruth from the Prussian Hohenzollerns, in exchange for ceding the remaining Wittelsbach lands on the Rhine. The Wettins were ultimately granted a "Duchy of Munster", created in the place of the former bishopric and some surrounding areas. They weren't happy, but, as said, nobody asked them.
The War of the Coalition - also known (especially in later days) as the Great French War or, in France, Great Patriotic War (La grande guerre de la patrie) - was finally over, as was the French Revolution. But the changes it, and the events stemming from it, had brought about irreversable, radical changes in all the spheres, alongside with more short-term, but still significant developments provoked by it.
Some of the More Immediate Consequences of the Great French War/War of the Coalition (if I didn't mention something, and didn't say anything to the counterwise, assume it still happened unless its totally illogical for it to happen):
I. Political:
- Complication of Franco-American relations (both due to the French political changes and due to the American shifting between Franco- and Anglophilic policies).
- Cementation of the Franco-Spanish alliance, growth of Spanish dependance on France.
- Spanish weakening, [comparatively minor] disruption of contact with Latin America.
- Continuation and worsening of the Anglo-French rivalry.
- Crippling and neutralization of the Dutch.
- Revival and reinvigoration of France, tempered by increasing internal instability (multifactional strife in the early 19th century).
- Termination of the Franco-Prussian rivalry, creation of the Franco-Prussian alliance ("Potsdam Pact", better-known in combination with the Franco-Spanish alliance as "Basel Pact").
- Rise of French overconfidence, as a result of this - an increasingly arrogant foreign policy and an assertive policy of colonial expansion.
- British overprotectiveness for Hannover.
- Perpetuation of Austro-Prussian dualism in Germany, general strenghthening of Prussia at the expense of relations with Austria, Prussian "shift to the north" and improvement of relations with Bavaria; also a minor shift to the Baltic and Poland, of not much influence yet (apart from lessening Prussia's chances of uniting Germany; it was tied down by Poles as Austria was Hungarians).
- Austrian weakening and paranoia.
- Italian uncertainty between Austria and Basel Pact; intrigues in Sardinia, the Papal States and the Two Sicilies as the three remaining key Italian states.
- Strenghthening of Russia by the value of the weakening of its neighbours and the Partititions of Poland.
II. Economical:
- Weakening of British trade in Europe, compensated by industrial development at home and strenghthening of trade ties in the greater world, especially in the Americas.
- Economic crisis in France, later relieved allowing France to exploit to a certain extent the crash of the Dutch commercial influence in Europe and the damage to the British one.
- Spread of Industrial Revolution to France.
- Continued rise of capitalism.
- Chronic economic crisis in Spain worsened.
- Temporary minor disruption of Italian economy.
- General strain of the war effort on the European economies, varying from place to place.
III. Cultural:
- Beginning of the Age of Nationalism, at first limited to Spain but gradually spreading abroad.
- General reaction against the Jacobin and other radicalism, initial rejection of many of the revolutionary virtues and values.
- Despite this, a later revival of radical sentiments and emergence of "Jacobinist" or Neo-Jacobin movements, especially in Ireland, France, Spain and Italy.
- Clash of die-hard conservative reaction and moderate/liberal post-enlightenment; though the latter ideas prevail in many countries, the Enlightenment ends.
- Time of cultural and ideological turmoil in France, to a slightly lesser extent the same in the UK (in part because it was believed that the naval mutinies - and the damn radical pro-Fox Whigs - cost Britain the victory), Spain and Italy, less so in the rest of Europe.
- Ascendancy of Romanticism in art.
IV. Technological/Military:
- Industrial Revolution sped up.
- Rise of the popular mass armies.
- Introduction of the concept of the levee en masse (gradually adapted in many other countries, fairly quickly in Prussia).
- With the new large armies, a shift from positionary warfare to mobile, decisive offensive warfare.
- Adoptation of loosely-formed lines as primary formation by some armies (including French and Russian).
- Rise of meritocracy.
- Introduction of aerial reconaissance (with baloons).
- Standardized-pattern firearms adapted.
(OOC: But generally, slower development of both weapons and doctrine than in OTL due to the lack of Napoleonic Wars)
And, ofcourse, lots of social strife everywhere, as one can predict. Next up, the early post-war era, with at least two major althistorical wars. Is anyone who isn't an Ailuropoda dementis reading this, btw?
dunno how i got the 2 mixed up
(), you also have a capsicum annuum reading it. 
