6...c4 isn't so good for black, Ne7 is the standard move.
French - Winawer

lol, first time I played the winawer I played 6...c4 too, thinking c5 needed to be defended. It's actually a pretty terrible move played so early, and 7 Qg4 gives white a pretty big attack. After 6...Ne7 7 Qg4 you can play ...Qc7, trying for a c file counterattack, or you can castle like I do, trying to disolve the attack and play against white's pawns and play for ...f6 or ...f5 to block lines. In both cases black gets counterplay but you have to be careful because white can still get a strong attack. 7...Qc7 costs a pawn but gives black the initiative and is hard to play against.

an alternative is 6...Qc7 ( with the idea that if 7.Qg4, then 7...f5). The Ne7 approach is famous for explosive bloodbaths with both sides trying to sacrifice everywhere.

6....c4 is very poor for black , black has much better moves at move 6... Ne7, Qc7, Qa5, b6 are all better than c4.

Ahh, the French Winawer Poisoned Pawn. Many a fond memory, epic games, fun to play, once as highly analyzed as the Sicilian is today. Played correctly it's a fun battle for both sides with a variety of choices. Fashion changed (Karpov v. Korchnoi), and the Tarrasch came about as it was easier for White to hold an advantage. Now Black likes to play 3... ed against both Nc3 and Nd2 heading for the "Fort Knox" setup and a draw as it is less to study, less tactical and easier to hold.
As to the original question, after 6.... c4 black goes back to his opening books, dBases whatever to find the correct plans and chooses one of them.
Where does black go from here?
Are there certian advantages for the Winawer that the Tarrasch does not have?