French Calvinists fleeing religious persecution choose to settle in Louisiana en masse, gradually turning the mississippi valley into a francophone heartland.
Let's assume this doesn't cause too many butterflies in european affairs (shouldn't, really.)
Seven years' war rolls around, and French Louisiane has the sheer manpower to effectively defend itself from Anglo-Brit conquest.
Maybe another POD here involving the French thwarting British attempts at scaling the heights of Quebec.
The result is a strong, more or less self-sustaining French colonial presence in North America.
The Thirteen Colonies are turned into a highly militarized march by the British, and they gain plenty of experience fighting the French over the following decades.
Eventually the Anglo-Americans prevail and annex the French colonies. The colonials agitate for independence and put their well-honed martial skill to excellent use against the British, who are trained only for organized European warfare.
Et voilà