Colonial Demographics of Franco-British Empire

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.
 
That depends tremendously on how much of France the King of England rules.

If the King of England merely controls (for instance) Normandy and Aquitaine, that will be a highly unstable state where the Norman-imported nobility of England, rather than converting to speaking English as in OTL, probably continues to speak Norman French, due to not losing almost all of England's territory in France. Under those circumstances you have a dominion where the English are the majority but French-speakers are a ruling minority all over the land and a majority in a small portion of the land. This state is also likely to be a constant enemy of France proper, and that's a war which it will very likely lose. If France proper has become a late-HRE-esque mess where the various French dukes, princes, counts et cetera politely pretend that the King of France is in charge while actually ignoring him and acting as though they were independent kings, I suppose such a dominion could survive, but goodness knows what sort of thing could happen then.

If the King of England is also King of France, the same thing happens with the Norman nobility of England, but the state is now not only ruled by a French-speaking class, it is also majority-French by a very great degree. Under those circumstances England will be more like an adjunct to the Kingdom of France than an equal partner—there would be a 'King of France and England' in the same way as the OTL 'King of France and Navarre'. Colonies would almost certainly be French-dominated; English people would go there too but the majority of settlers would be French, and even the English people in England, let alone those surrounded by a French majority in the colonies, might be fairly Francified. There might be regions of colonies where the English were more present, as there were regions of OTL North America where there were a lot of Scotch-Irish for instance, but I do not think there would be separate English colonies. The greatest danger in this case is that such a state might not long survive; the King's ability to impose taxes on the French without a parliament that he needed for the English would be resented by the English, and there might well be an English rebellion, leading to a France ruled by the House of Lancaster and an England ruled by the House of York.
 
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