At the time of the Revolution, Canada consisted of various colonies that would later be called British North America after 1783. These colonies included Rupert's Land (northern Quebec west to the Prairies and far to the north), Canada (modern day Quebec/southern Ontario), Saint John's Island (Prince Edward Island), Newfoundland, and Nova Scotia.

Let's now refer to "Canada" by what geography it involved at the time: Quebec/Ontario/parts of New Brunswick.

Canada was conquered by the British in 1763 during the Seven Years War. The war culminated in a battle over Quebec City known as the Battle of the Plains of Abraham. While the battle lasted just under 20 minutes, it was brutal and both the French and British generals were killed. Afterwards, the French fell under British rule and the British deported the Acadian people (French-speakers in the Atlantic provinces) either back to France or south to Louisiana. That's why you have a French culture in that state. "Acadian" eventually got corrupted (in linguistic terms) to "Cajun."

Alright, that's a bit of background. So the French are living under British rule, and certainly there were thoughts of revolt among members of the French population. This is especially true because, you're right, Canada's population was overwhelmingly French. If they had organized, they might have launched a successful Revolution of their own. Since that's taking a lot of different assumptions into account, we'll set that idea aside and focus on your main question.

It's interesting to note there was a fair amount of distrust between Canadiens (i.e. Quebecois) and les Bostonnais (not just meaning Bostonians, but the entire Thirteen Colonies). Members of the Colonies were British regulars during the Seven Years War mentioned earlier. You may also know it as the French and Indian War. The mainly Protestant Americans helped the British defeat and subjugate the predominately Catholic Canadiens, so a few years later when the Americans needed help, the Canadiens weren't so inclined to pitch in.

And the real biggie? In 1774, Canada was divided up a little more and the Province of Quebec was incorporated into the British Empire. This is covered in the Quebec Act, 1774. Some of the conditions are outlined below. Keep in mind, this is from Wikipedia:

1. The province's territory was expanded to take over part of the Indian Reserve, including much of what is now southern Ontario, Illinois, Indiana, Michigan, Ohio, Wisconsin, and parts of Minnesota.

2. Reference to the Protestant faith was removed from the oath of allegiance.

3. It guaranteed free practice of the Catholic faith.

4. It restored the use of the French civil law for matters of private law, except that in accordance with the English common law, it granted unlimited freedom of testation.

5. It maintained English common law for matters of public law, including administrative appeals, court procedure, and criminal prosecution.

6. It restored the Catholic Church's right to impose tithes.

To make a long story short, Canada's role in the American Revolution really came down to whom the Canadiens chose to side with. In essence, the British won neutrality from the Canadiens by signing the Quebec Act and making small appeasements to the French population. Quebec has always sought some form of autonomy or independence, but for now, it was at least somewhat satisfied with the terms. Unfortunately, Canadiens still had a bad taste in their mouth from previous encounters with the Americans in the Seven Years War.

As an aside: see how the Quebec Act gave Ohio and a few other modern states to Quebec? Yeah, the Americans were not pleased about that. The Act was a contributing factor to growing resentment and revolutionary talk.

In 1775, the Americans attempted to invade Quebec but were largely unsuccessful. American privateers also raided seaside towns along the coast of Nova Scotia and Saint John's Island (no small feat, that was deep in enemy territory). These attacks helped solidify the position of most Loyalists (French and Anglo Canadians loyal to the Crown) and inspired more support for the British to quell the Colonies' rebellion.

EDIT: Spelling error. Switched "autocracy" for "autonomy" thanks to a keen eye. Nobody likes autocracy except the autocrat!

EDIT 2: Clarified the aside related to the Quebec Act thanks to another keen eye.