Napoleon, shortly after taking power, is shot by counter-revolutionaries, and a few other individuals are able to make peace with the rest of Europe without giving too much away, and are able to solidify a long lasting (if shaky and sometimes autocratic) democracy in France. France is later able to smash through the dying Holy Roman Empire (still alive up to the 1850s), and a new wave of revolutions spread through Europe afterwards.
Anxious to prevent revolutionary fervor from spreading to Spanish America, the Kings of Europe send off some of their relatives to become kings of new kingdoms sprouting there (in some places, a local made himself king). A wave of revolutions later spreads there.
Today, there are three main blocs. The most powerful, by far, are the Radicalist Republicans, who now dominated Europe. They're democratic, if a bit more leftist than those nations are OTL. Religious groups are more prone to claim that they're being officially discriminated against by the secular elite. Picking up revolutionary fervor, are abused nations in Asia and Africa. These are less nice places to live than the welfare states of Europe. Brazil overthrew its Emperor in the last decade, and has brought in a new Radicalist Dictator, whose cultural revolution echoes that of Mao. France was able to keep part of Louisiana longer, and regain Quebec, and so those territories are now some of the nicer Radicalist republics.
The Conservative Republicans, lead by a weaker, more inward looking, commerce minded U.S., are slightly more conservative than OTL, and also still Democratic. The U.S.' first major intervention in a foreign nation occurred this past decade, and many in the U.S. still oppose it, and support greater isolationism (though there were wars in Europe similar to the World Wars, they were smaller, and the U.S. never got involved). The U.S. doesn't have the global clout is does in our world. It has a bit more emphasis on states' rights (there never was a civil war), and the two major political groups are the 'Union Party', and an alliance of regional parties (that's simply called that). Mexico is more powerful, and is friendly with the U.S., and is similar ideologically, but lingering territorial disputes prevent it from getting much closer.
Russia, on the losing side of the last war in Europe, has gone full blown autocratic. It's still ruled by a Tsar, who now also acts as head of the Russian Orthodox Church. Russia is nuke-wielding, clerical fascist. It keeps a string of states, whose rulers it props up, around it, and even supports the Orinoco Kingdom, far away (a perpetual inquisition state). Russia was able to nip Japan in the bud, before it industrialized. The Sino-Russian border is one of the most militarized on earth.
Parts of the world exist outside of the big three. Arabia, is united under a nationalist theocratic democracy (only about as corrupt as modern day OTL India), that's been growing big recently. Hungary-Serbia, is a constitutional monarchy, and wealthy neutral state ruled by a local King and by Parliament (it's much richer and filled with less ethnic conflict, thanks to less nationalism, than that part of the world OTL). And in Africa, and the Statocratic Liberation League of Africa, plots to create a new master race of humanity (probably black) and unite Africa into a single machine (with other wacky, weird stuff, like the replacement of Christianity and Islam with the personality cult of the dictator and soviet-style atheism). Italy is an enlarged papal state.