I think the most "French-like" reply to 1.d4 is the King's Indian Defense. By playing an early ...e6 and ..d5 you're making the same moves as in the French, but you hardly ever get a similar type of pawn structure.
However, with the King's Indian, you'll often get a closed center with a chain of blocked pawns on it, with each side playing on an opposite side of the baord, just as in so mnany variation of the French.
