It depends on geographical dispositions of this new population to an extent. The province which had the best chance of developing a strong french population in OTL but didnt is probably Manitoba, which had many French-speaking métis. You can have a strong French minority there easily. Also, if you lessen a bit the extent of the Acadian deportation, you end up with substantially French-er Maritimes. That kind of disposition would likely prevent breakups basic of ethno-linguistic reasons, whereas a stronger territorially continuous bloc of relatively homogeneous French-speakers logically encourages it.
French Quebec doesn't really believe in the idea of a bilingual federation because French was essentially stamped out of the rest of the country through closure of French schools and Anglicization of French communities, etc. This is largely what created what we call the "Two solitudes". Logically, changing that is a way to have a more bilingual Canada.
One step towards a more united truly bilingual Canada would be to have all the provinces agree to make both languages part of their core education curriculum - or to constitutionally make that an obligation from the start. All this takes quite a bit of goodwill and long-term vision I suppose, but it gives the best ending as far I'm concerned. A higher percentage of English Canadians who speak French well and like the language would probably help solidify the country quite a bit.
The other way is simple demographics. Keep the languages largely separate and at odds, but have more French kids and less English immigrants. In this scenario, though, you maintain a French majority for several more decades. That likely means that London would delay both self-rule and Dominion status for Canada, and make at least another 1838-style revolt a possibility. That scenario also increase the odds of eventual tensions and referendums.
So I guess my point is: How you get your 40% French Canada matters alot in determining how this would play out.
