Why would this last - I'm not arguing, just looking for elaboration - meaningfully change things?
At first I had written a longer description, but realized that it might very probably lead simply to OTL, just nudged a bit earlier.
My thinking was: in the Great Lakes and what is now the Midwest, the Indians were able to play the French and British against one another. The French were more adept at drawing allies because Canada was not the settler society that the British seaboard was - its settler population was always just a fraction of that of the English speaking colonies. This meant that (1) France had more reason to seek allies, and (2) the Indians were more inclined to work with the French, because they were so much less land grab-y.
So get the French out of the way sooner, and the British settlement wave hits that much earlier, the tribes in the Great Lakes and the Ohio country have less time to react, the population of New France is even smaller (so you might end up with an English-speaking Quebec) and in general the settlement patterns of OTL are put on fast forward.
Maybe not a dystopia, but in all likelihood worse than OTL.