During the period of Colonial America, France had claimed a much larger portion of land than Britain, but the flip side is that most of it was uninhabited by the French themselves (instead populated by Natives). While Britain's claim was smaller, it was much more heavily populated by settlers: 2.5 million British colonists vs. about 70,000 French colonists at its peak. Despite the vast amount of land seen above, the real strongholds of the French were Quebec in modern day Canada, and Louisiana in the American south. Other than that, the only real footprint left is that a bunch of cities and towns in the Midwest have French names without possessing a French identity (such as Detroit or St. Louis).
The reality was is that France saw their claim to the Americas as more of a business and military investment, then as a place to settle in large numbers. Indeed, it's said they never really cared that much about it, hence why they eventually forfeited their claim just to secure a few rocks in the Caribbean. That's why even if France won the French and Indian War, it's highly unlikely that they would be able to invade and conquer the British colonies, because they simply wouldn't have the manpower to do it.
But what if the New France settlements actually saw a much larger migration comparable to the British? What would it change to multiply the number of French colonists in these areas, and could that have happened?