What if the French king had fled to Lousiana from the Revolution?
I doubt it would've affected the tide of war in Europe, but in America, there would be the Kingdom of Louisiana (probably it will work like this - many French immigrants would follow their king there, when the Republican French overrun Spain they request that Louisiana is granted to them, the Spanish agree, but the king and his followers rebel from the Spanish. Btw, to make this easier to mod if accepted, I will reduce the amount of South American nations by having San Martin die in the Spanish army). The French will have less war funds without being able to sell Louisiana, but they will still have a half of Haiti and sell it instead. So, if we suppose that the war in Europe goes the same way, French king will return to France and grant Louisiana independance under some troublesome relative just to send him away. UK meanwhile wins the War of 1812 without being distracted to New Orleans (Louisiana even enters the war on British side in the very end, but failed to make any territorial gains), and grabs parts of Maine, plus Minnesota and Michigan territories. Bolivar's rebellion created an independant Gran Columbia, which eventually grew to expand to all of Central America and to Peru. De La Plata remained Spanish, some believe this to be the only reason that prevetend Gran Columbia from falling apart.
Later on, when in 1836 the Texan Rebellion was near death, Texas pleaded for British help, asking for Dominion status. The British eagerly used the opportunity, and by 1839, Mexico surrendered unconditionaly after mass bombardment and several landings. Dominion of Texas gained Colorado and New Mexico, the British annexed Yucatan and California. However this distraction of forces prevented the Opium War from ever happening as the British choose to negotiate with the Chinese instead of attacking them. USA and Louisiana fought several inconclusive wars, while in Oklahoma, Louisiana and UK created an Indian (New World, ofcourse) nation.
Back to our Chinese friends, eventually a civil war occurs, when the Taiping forces overrun China. However, the promised equality does not come and China returns to isolation instead. Enraged (as trade with China DID bring some profits), the British, Russians, French and Prussians intervenne in 1869. The Taiping forces are crushed, and China is divided into protectorates - Russia gets Sinkiang, Mongolia and Manchuria, British get Korea and southeastern coast plus Tibet, the French get the southwest, while the northeastern China Proper, including Beijing, went to Prussia. However, heavy resistance continued in most of China, and actual control is, for the exclusion of Russia's, only in the coastlines (and Russia too has much trouble in Manchuria) - the rest is in anarchy.
In 1871, the Prussians have invaded France, but suffered large casualties as the French have perfected the machine gun from the times of the Taiping War. Fighting degenerates into a trench war in westmost Lorraine-Alsace Eventually, however, the Prussians ally with the Americans and blockade France - UK lets it go when it is promised that France is not completely destroyed as a great power, and accepts the bribe of the French Algieria. French tire out, and the workers rebel, declaring the French Commune. Prussians crush the regular French forces in 1873, and the French communist government ceded whole Lorraine-Alsace and Morocco to France, Tunisia, Nice and Savoy to Italy (which entered the war by then), Algieria to UK, and Caribbean possessions to USA (oh, and note that no Civil War happens and gradual emancipation is declared in 1876, as Lincoln was never elected president, having died in one of the wars with Louisiana. Thus, secession is still constitutional).
Russia eventually does abolish serfdom, just as in the real history, and Duma also appeared. Luckily for Russia, gold was discovered in Alaska in 1886, causing a (limited) gold rush there, followed by analogical ones in British territory in the Greater British Columbia (British Columbia+Alta and Baja California). Russo-Japanese war in 1899 (result - overwhelming Russian victory and annexation of entire Japan as Japan never opened up and was horribly outdated) nearly caused a Russo-British one, but it was avoided and Russia ceded the two southern islands to UK in exchange for neutrality.
USA continued on its policy of acquiring the Carribean Sea. This led to a war with Spain, with Germany on American side. This ended with the American acquisition of Haiti (lol, it got in the way), Puerto-Rico and Cuba, while Germany took the Philippines.
Despite the best hopes of many governments across the world, France did not collapse and counter-revolution failed. French Commune soon expanded into Spain and Portugal, and in the best spirits of internationalism declared the West European Commune, annexing the two nations. De La Plata declared an independance, becoming a Jesuit Dictatorship.
War is coming, and though the sides are not yet picked as the world enters the 20th Century, they soon will be. For now, diplomacy continues as usual, but soon it might be extended into WAR!!! (tm)