Two things to add.
First, that if Great Britain were trying to sustain the balance of power in the settlement after the Seven Years' War then it did an awful job of it. It grew so incredibly powerful that virtually every other power in Europe formed a coalition against it at the next available opportunity and even its ally, Prussia, which had a strong interest in keeping Great Britain powerful lest the issue of Silesia be resolved in favour of French-aligned Austria, didn't step in on its side. I generally tend to find that people attribute "balance of power" thinking much more strongly to the British than is actually based on the available evidence; I suspect that much of this tendency comes from British concern about the balance of power in the latter half of the 19th century and the pre-WW1 20th century, but there the term was used (at least in Disraeli's famous speech after the Franco-Prussian War) as code for "keep Russia weak because we're rivals with Russia", rather than any genuine concern for stability.
Secondly, though I'm not sure if this is entirely on topic, I've read many times that British America and its English predecessor were far more populous than the French colonies in North America, and though I don't dispute it for a moment I've never read an in-depth and convincing explanation of why that was so. After all, the key elements—dedicated religious elements more radical than the monarch and dissatisfied with religious repression in their homeland (Puritans/Huguenots), a thriving network of trade (including rather more trade with the Native Americans than the British ever had), good ports (though not as many) and vast tracts of land to settle—were there. The main differences I can think of off-hand are the more temperate nature of the lands England and later Great Britain controlled and the more aggressively expansionist English/British policy towards Native Americans, as opposed to French policy, (the seigneurial system's importance is I think much-exaggerated, as most of the French colonies' income and appeal came from those who were not subjected to it) and off-hand those seem fairly reversible with a reasonably early PoD. The point that others have raised here, that the French disadvantage in population was France's main disadvantage against the Anglophones in North America, seems clear to me, so surely, if France is to do well, we need to undo or perhaps even reverse the population imbalance, and for that we must understand why it was as it was IOTL.