Allow Huguenot settlement, New France becomes more densely populated from the beginning, with an institutional and customary religious tolerance, and southern Ontario also remains Francophone. Eventually either it breaks away from France or is conquered by Britain. If the latter, I see a larger French population being less tractable than the fairly few Canadiens of OTL. So, possibility of a revolt there, supported by France and the US*, which then establishes a secular republic and attracts especially Catholic immigration, with the US* still very much nativist and dominated by English-speaking Protestants. Whether this includes the Atlantic Provinces is open, but Acadia might also get Huguenots in this scenario.
Next, waves of immigration from Europe and missionary activity in the west. Canadiens of both Catholic and Huguenot belief compete for souls a among the First Nations (Metis come in both flavors and often intermarry), along with Scottish, German and Scandinavian denominations, followed afterward by Orthodox East Slavs, who are also quite unwelcome in the US*.
Asian immigration becomes a hot button issue, but with both a more secure and unified Canadiens culture and a history of respect for different beliefs, exclusion never takes off as OTL. Alaska might be purchased for some paltry sum, or seized if Russia loses a war or experiences a revolution. Gold, gold everywhere.
So, there you go: Republique du Canada of maybe forty-forty five million persons, likely mildly dominant Catholicism, perhaps less repression of First Nations (I'd have to elaborate this, but the French tradition was to coopt native nations, rather than dispossession and extermination, but this might change with a real settler colony and independent statehood), greater numbers of East Asians (although perhaps fewer South Asians, without the British connection) and a valid cultural competitor to France itself.
How do you like them apples?