In a situstion where the King of England controls sizable portions or all of France, what might the demographics of such a kingdom's colonies in the New World look like? Consider religion, ethnicity, language, and political organization.
Would it be more likely that each portion of the realm would run its own colonies, so that you'd see swaths of territory either French of English, or would it be more likely for tjings to be more blended? On the one hand, it might seem natural for colonies to stick to what is familiar and segregate themselves by their origin. On the other hand, so many colonies were first and foremost about economic bounty that many might be willing to strike out into culturally-dissimilar regions. The US, of course, is the best historical example of this.