alternatehistory.com

The Seven Years War goes a little differently, and Britain doesn't take all of that French territory on the other side of the Appalachians. Maybe George Washington also dies. The American Revolution still happens, but the French are in less need of an opportunity to get back at the British, and don't intervene. The British win and crush the rebels. The colonies mostly retain self-government, and are given a few token seats in parliament, but traitors are punished severely, and the colonies are forced to acknowledge that what powers their local governments do have are purely the gift of king and parliament, not something springing from a fundamental right to self-determination. Post-war there is a lot of bad blood, and so a lot of American patriots start fleeing to the other side of the Appalachians, outside of British control. The French look more kindly on this than they would have in an earlier era, since they see these immigrants as implacably anti-British, and thus a potential barrier to British expansion into the relatively lightly populated French territory. While technically in a less 'democratic' society than the one they left, the new colonists are sufficiently far from any effective authority that they're able to essentially govern themselves without too much issue.

The French Revolution still happens, different in detail but similar in broad form to OTL. The Americans settled in French North America are generally quite pro-Revolution, since they are by definition the kind of people so committed to the failed American Revolution that they'd rather flee their homes than stay under British control. When war breaks out between Revolutionary France and Britain there are a number of skirmishes all along the border, and some rumblings of pro-revolutionary sentiment in the colonies, but neither side feels up to really conquering the other, so things stay quiet for the moment. As increasingly democratic constitutions are passed in France, the colonies begin trying to emulate the mother country. There are more French settlers ITTL due to longer control, and joined by the westward moving Americans, both the ideologically motivated and those who just want free land, they form their own little elected assembly. This assembly has the advantage that it is a long way away from the center of the action, so while successive waves of revolutionary terror sweep through France, the colonial assembly just gets on with business. The most pressing business is of course preparing for any potential counter-revolutionary attack, but many are also caught up in the spirit of the times and are eager to reform their scattering of colonies into a real Republican partner for France. They affirm human equality, institute elections on the basis of universal suffrage (well, except the Indians, let's not get crazy), abolish slavery, and form a continent-wide government with a fair bit of power – roughly comparable to the early American federal government of the same era OTL in terms of levels of power reserved for the central vs provincial governments.

As time goes on and the revolution falls apart, French North America pursues an increasingly independent course. After Napoleon declares himself Emperor and the still very Republican FNA government had had about enough, and started looking for an exit. Luckily for them, an exit was not too hard to find. In exchange for renouncing their now only de jure allegiance to France, the FNA makes a separate peace with Britain and quietly slides into official independence without anything much changing on the ground.

The Napoleonic Wars come to a close with Napoleon defeated, and order is finally restored to Europe. The revolutionary types who once seemed so ascendant now have only one friendly place left to go: what was French North America, and what by this point begins to call itself Canada. Republicans fleeing restored monarchies all across Europe make their way to Canada, along with the usual stream of less ideological immigrants. In addition to this flow from Europe, a great deal of immigration continues from the British colonies to the east. Land hungry settlers have no problem hopping the border, persecuted Indian tribes flee to the less densely populated and marginally more tolerant Canadian side of the border, and slaves flee in droves to a land where to set foot on the soil is to be a free man. Some forts are built by both sides to try to prevent, or at least regulate, some or all of this movement, but prove totally ineffective. Canada's population and power would continue to grow, particularly relative to its North American neighbors, for a long time to come.
Top