When the 13 colonies revolted against the British Empire, it seems that a natural ally against British rule would be French-Canadian Quebeckers. They had only recently been under British rule after the French and Indian War and I cannot imagine French colonists enjoying life under English-speaking Brits. But French colonists did not end up joining the 13 colonies in rising up against British rule, even as France became an ally to the 13 colonies.
So why? Why didn't the French-speaking population in Quebec join their 13 neighbors and their former mother country (France) in waging war against the British?
You can find more context on Quebec in the aftermath of the Seven Years War and the years preceding the American Revolution in this post by u/enygma9753.
The habitants (or Canadiens as they were also known then) had forged an identity distinct from France over the 150-year history of New France, despite similar cultural ties and Catholic faith. After the British conquest, France chose to keep sugar-rich Guadaloupe over Canada during the 1763 peace negotiations in Paris. This generated feelings of resentment in Quebec over France's readiness to abandon its colony to British rule. Some even saw it as a betrayal.
The British had anticipated a wave of English Protestant settlers that would overwhelm the French Catholic population (about 70-80,000 in 1763) and assimilate them over time. This didn't occur and the French Canadians outnumbered the English in Canada by 25 to 1. As tensions simmered to a boil in America, the British knew that they had little hope of containing an open revolt in Quebec if they antagonized the habitants.
Prudence and accommodation were seen as the way forward to keep the peace, culminating in the 1774 Quebec Act, which guaranteed French language, property and civil rights under British law. It also gave generous accommodations to the Catholic faith and church institutions -- unheard of even in Britain itself, and regarded as offensive to the sectarian Protestants in America. The Act would become one of the 'Intolerable Acts' that would spark rebellion in the Thirteen Colonies.
The habitants didn't trust the British, but they had loathed the American colonists, who were their continental rivals and bitter enemies for more than a century of conflicts for resources, land and imperial ambitions. There was no love lost there among many French Canadians, although some locals did look favourably on the Patriot cause and enlisted in Continental units.
Vague Patriot offers of liberty were largely seen as not worth the risk of losing their actual rights as British subjects. Benjamin Franklin's overtures in Montreal to join the revolution met with skepticism.
The church hierarchy, which had tremendous influence, also reminded them in Sunday sermons that republicanism was the path to anarchy and that excommunication from the Catholic Church was the price of aiding the rebels.
The habitants calculated the pros and cons and, by 1775, prudent neutrality was the result.
The revolution was a dispute between two groups of English Protestants in their eyes, neither of whom had earned their affection. Although they had taken an oath to the king to keep the peace in Quebec, this didn't mean they would bear arms for England either.
Fear of assimilation, mistrust of the American rebels and satisfaction with Britain's peaceable -- if imperfect -- rule in Canada all contributed to Quebec's pragmatic choice in 1776.
Most American colonists were very anti-Catholic, and the Quebecois saw them as a larger risk to their religious and political freedom than the British, who at least tolerated their Catholicism.
The Quebec Act of 1774 restored many of the rights the French residents of Quebec were chaffing under (free practice of the Catholic faith, restoration of French civil law for matters of private law, the restoration of the Catholic Chruch's ability to collect tithes, etc.). This act angered the American colonialists to the point that it was deemed one of the Intolerable Acts due to it's additional provisions of land in the Indian Reserve to Quebec. The Americans actually called for it to be repealed which angered and scarred the Quebecois.
The Quebecois and American colonists were at odds from the begining and the Invasion of Quebec by the Americans did nothing to aleviate Quebec's fears of American nationhood over Quebec.