I would have thought you would be sympathetic to the idea of creating a North America that has more (much more) space for Native and mixed peoples, Shevek. I have to freely admit that I was inspired by False Dmitri's Affiliated States of Boreoamerica setting and the idea was to find a plausible method of reaching somewhat the same end of having a massively pluricultural North America with much larger Native populations and more Native cultural influence.....
Sympathetic may have been the wrong word. An ATL where Native Americans could develop a complex of societies engaged with the European global system but not crushed by it would be nice I suppose. I am somewhat disinterested as I am pretty invested in something like the USA existing, to the point I have a hard time wrapping my head around North America without it being a superpower.
And mixed up in my honest disinterest in working out voyageur-America (I might enjoy spectating at the result to be sure) was my lack of sympathy for the idea that the English could be kept from settling Atlantic shores. As you said, if the king is king of both France and England, he has to listen to the interests of both. The English interest is go off and colonize somewhere or other. You might divert them to a different location but the dual monarch would be a bad king of England if he reserved North America for the French model alone, unless he compensates the English with something to make up for their lost opportunities.