This is a request map done for Jeckl.
In this world, a slightly different US revolution sets the butterflies flapping. The French revolution proceeds a bit differently, and France remains a Republic, albiet an authoritarian, paranoid, guillotine-happy one. Napoleon dies as a traitor to the Republic.
Butterflies flap back across the Atlantic, and a war of *1812 goes worse for the US than OTL. New York and New England, and later New Jersey, break away. The US becomes a Greater Confederacy, agrarian, slavery-based, with a weak central government. It still expands, south and west, and slowly swallows a civil-war torn Mexico.
The French Republic is less immediately successful than Napoleonic France, but it does a better job of holding what it has. It gives Spain a terrible drubbing, but avoids an occupation, merely detaching the Catalans, and holds off Russia and Austria to the east. Prussia is permanently crippled. It maintains appeal as an inspirer of revolution: later, a Republican revolution sweeps Spain with French aid: the new Spanish republic will later swallow portugal. French client states in Germany are allowed to join, creating a powerful new buffer state. A new round of revolutionary wars see to the formation of a large, independent Poland.
While the British and French are distracted with mutual quarrels, as in the previous partitions of Poland, Austria and Russia devour the Ottoman's European territories. Russia creates a new "Byzantine Empire" out of Ottoman territory, it's capital at Constantinople, a handy extra Romanov plunked on its throne. The by then independent rump Greece is infuriated: after a couple bloody clashes a pissed of Tsar of Constantinople annexes all of Greece.
The French and British, late to the feast, will gnaw on the Asiatic portions of the dying Ottoman body. Constantinople will remain Muslim majority until the early 20th century, when the anti-European revolutions that finish the Ottomans off spread to Byzantine territory, and the Great Expulsion takes place.
Britain and France find proxies in the east in the form of Japan and China. With French support, China manages to avoid the collapse of OTL and makes a painful transition to a sort of limited monarchy, albiet one shaped by the oddities of French "democracy."
The New Englanders become a steady British ally, and get into the colonialism game, supposedly for reasons of "the civilizing mission" but also for supposed financial bonuses and national prestige.
Come 1937, things have been in a state of "cold peace" for a while, aside from the recent Unpleasantness in Korea, but nobody is sure how long it will last.
France has mellowed a bit since the times of the Terror, but it is still a rather authoritarian and paranoid society by our standards, and although there are elections and so on there are a rather limited number of legal political parties. There are high standards as to what one owes The People, military service is universal, and the bureaucracy is formidable, as is the secret police. Children are indoctrinated in school as to the superiority of their system and the corruption of all others. A vigorous effort is ongoing to make Africans into brown Frenchmen, whether they want to be or not.
Religion is rather different from OTL: France is less secular than our version, but Catholicism is supressed as a foreign influence (the Pope is well outside French-controlled territory). Instead, the Cult of the Supreme Being has developed into a rather developed, if weirdly rationalist, national deist faith, along with a "cult of reason" and science as impenetrable as Vulcan philosophy. Actual athiesm is looked upon with a certain degree of suspicion, because such people are also likely to disbelieve in The Will of the People or the Inevitable Course of History in a revolutionary directions. Protestants, of the drier, less enthusiastic and more hard-working varieties, are acceptable, as are the mystical, anti-Papal National Catholics, although they clash with the worshippers of Reason. ("Battle Philosophers" is a popular radio show in France and west Germany).
Relations remain poor with Britain, which is generally less democratic and more reactionary than OTL 1937, in reaction to French republicanism: there are still property qualifications on the vote. Unlike our world, the UK has a very large standing army, to repel any French invasions and also to deal with any radical revolutionaries. The British upper classes tend to look with a rather jaundiced eye at the fairly democratic government of their new England allies (which is, however, a bit oligarchic by our standards)
Austria is perhaps the most "progressive" nation in Europe, and has developed a federal structure of many small provinces with local autonomy on things such as language rights, thereby defusing some of the irritants of a German-dominated empire while not creating large national blocks which would encourage seperatism and by existing create local, smaller-scale irredenta. It's inhbitants nowadays probably have more freedom than the citizens of France, French beliefs of it as a feudal remnants nowithstanding.
The Tsars went the populist route in maintaining popular loyalty, only to find themselves somewhat sidelined by nationalist politicians of the far right (the only legal parties in the Duma vary from right-wing to barking mad rightwing). Jews continue to have a hard time, and emigrate in large numbers to Austria, the French sphere, or the British empire.
The revolutionary Saxon republic has created a new sort of technocratic one-party left-wing "republic" for the 20th century, and their enthusiasm for purges is creeping out their French sponsors.
Realpolitik has led France to form an alliance with the Commonwealth of Columbia, in spite of dislike for their racist policies  and rather irrational attitudes: with Russia growing both in industrial power and nuttiness, steps need to be taken to allow for concentration of forces in the east: an effective anti-British deterrant is important.
Columbia has a weak federal government, about the only thing it actually has nation-wide rights to tax for is the maintenance of a military strong enough to keep the Mexicans down and the British and New Englanders out. Local laws and levels of democracy vary widely, varying from near police state to almost anarchic (well, for white people, anyway). Mind Your Own Business is the law of the lands, big business is powerful, and dueling is still legal in five states, most notoriously Texas.
"Official" slavery was finally put to an end in the 1920s, but blacks and hispanics who can't "pass" are under so many legal restraints that they are little better off, and various forms of debt-slavery and peonage exist even for white people. White population decline is a hot topic, and various states have passed laws encouraging more white children and taxing singles who don't reproduce, although a national "bacheleor and spinster" tax remains contentious. A great deal of sterilization of blacks and insufficiently white hispanics takes place, much on the sly, for a variety of excuses.
Presidents are essentially for life, being indefinitely reelectable and the election process being richly corrupt and highly favorable to incumbents, but high assassination rates and the usually elderly nature of candidates picked in smoke-filled rooms mean that few last over a decade in office. Currently, the Nationalist Party is riding high, and are working to create a more unified and effective nation by taking over the political machines, one state at a time: they have had considerable success east of the Mississippi, but less so in the west: Texas in particular has seen quite a few political operators ridden out of town on a rail, often after a good tarring.
The "New Republicanism" of the late 1800s, aside from seeing the name change to the Commonwealth of Columbia in a symbolic effort to promote a more unified nation, saw the flourishing of a national "Columbian" religious movement, in imitation of the French state cult, which although never able to displace the wild variety of protestant cults and groups which flourish nation-wide, came to exist beside them somewhat the way state Shinto co-exists with Buddhism in Japan. The founding fathers have become venerated as saints, heaven-sent to create the greatest of nations, and immigrant Russian icon painters have adapted to demand to create household shrines to Washington, Jefferson, etc.
(China, too, had developed some odd new variations on traditional state cults...)
 Racism is irrational, and France is a nation of reason, so therefore any denial of rights to Africans Arab or black is of course due to perfectly logical and scientific reasons involving the dangers of irrational religion, bad cultural memes, insufficient education, etc.