Per Data, French is an obscure language in the 24th century. Picard may have learned it natively, because his parents appear to be native Francophones by their accent, and his father in particular may have been a bit of a luddite, but that doesn't mean the other villagers in La Barre spoke it on a regular basis. Picard need not go to a British boarding school to pick up English, if it was already the majority language of mainland France for generations.