With a POD in 1800 anything can happen. Two short ideas:
1. Napoleon somehow wins. He transforms his Empire to a multinational entity, with great liberties for the different ethnics. He does not invade Russia, instead Russia invades and is defeated. In his old days, Napoleon transforms the Empire towards a more consitutional monarchy. 1830 Napoleon resigns, his son is elected "Roman empire" by the French national assembly and delegates of the Confederation of the Rhine. almost a century later, the Roman Empire fights a war against Britain and whoever you like.
2. In 1866, Italy is much better prepared than IOTL, as is Prussia. Austria is even weaker. No matter what the reasons are. The Prussian-Italian alliance wins very fast and decisively and imposes hard peace terms: Italy gets Venice, Dalmatia, Istria and Southern Tyrol, the rest of Tyrol becomes independent, Prussia gets Bohemia and Moravia, Russia is appeased by eastern Galicia. Large parts of Austria are occupied. Napoleon III. is surprised and reacts slowly and dumb. He demands large parts of western Germany, which alienates the smaller German states which just fought against Prussia. They ally with Prussia against France, France looses due to incompetent leadership. The Prussians however never reach Paris, the Emperor is caught quite early, a revolution takes place, Bismarck urges for a fast peace to end the uneasy situation with a still occupied/fighting Austria and an uneasy Russia. Essentially this turns the peace treaties of OTL: Austria gets the hard one and becomes an enemy of Prussia/Germany, France gets a light one and is in the following years won as an ally as Austria was IOTL.