Black's biggest problem in the French Defence is his light squared bishop that often remains passive, restricted by the pawns on e6 and d5. The problem can be so bad that French players are often willing to spend several tempi in the opening just to swap it off, e.g. in the Winawer variation:
1 e4 e6; 2 d4 d5; 3 Nc3 Bb4; 4 e5 where Black plays 4 ... b6, intending to follow up with ... Ba6.
The trouble with this Winawer line is that White can utilise the time gained to either attack on the king side or build a big advantage in development, e.g. after 5 a3 Bf8; 6 Bb5+ or an immediate 5 Qg4.
I prefer the early bishop swap concept against the Advance variation (particularly as players of the Advance variation are typically the sort who love their light squared bishop hitting against h7). In the Advance, a small change in move order, delaying Nc6, is used to 'disguise' the bishop swap idea:
1 e4 e6; 2 d4 d5; 3 e5 c5; 4 c3 Qb6; 5 Nf3 Bd7; 6 Be2 cd; 7 cd Bb5
The bishops are coming off, costing White a key attacking piece, and the nature of the game becomes a clear battle between Black's play down the c-file and White's space advantage.
Note: Black played 6 ... cd first to avoid giving White the option to meet ... Bb5 with c4.
From this Kupreichik - Eingorn, USSR 1977 went:
8 Bxb5+ Qxb5; 9 Nc3 Bb4!; 10 Bd2 Qd3; 11 Qa4+ Nc6 with an equal game.
In my game against David Henderson from the Northumberland County Championships in 1994, David tried:
8 0-0 but after 8 ... Bxe2; 9 Qxe2 Nc6; 10 Nc3 Nge7; 11 Rd1 Nf5; 12 Be3 Be7 Black went on to win.