In truth: Patrick Stewart is English. so… yeah.

In Fiction: English is normally taught by the British in France. An Anglophile like Piccard (you’ll find out he’s a fan of many, many English writers) might have spent so much time speaking “the queen’s English” as to have lost all hint of a French accent (I can point to a few Indians and at least one Irishman I know who this is true for).

A second possible answer is that English has become the defacto standard in Star Trek, even in France. Or some combination of these two possiblities.