It's funny. Everyone always laments Black's passive light-squared bishop in the French, but I rarely can find effective ways to exchange it, and when I do, I miss it!
Here are a series of games in this line:
[Site "Bielorussia"]
[Date "1963.??.??"]
[White "Rubenchik,A"]
[Black "Goldenov,Boris Petrovich"]
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 Bb4 5.e5 h6 6.Bd2 Bxc3 7.bxc3 Ne4 8.Qg4 Kf8 9.h4 b6 10.Bd3 Nxd2 11.Kxd2Ba6 12.Ne2 Bxd3 13.cxd3 Nd7 14.f4 h5 15.Qf3 g6 16.g4 Ke7 17.f5 hxg4 18.f6+ Ke8 19.Qxg4 Nf8 20.Nf4 c5 21.h5 gxh5 22.Qg7 Rh7 23.Rxh5 Rxh5 24.Nxh5 cxd4 25.cxd4 b5 26.Qg8 Qa5+ 27.Ke3 Qc3 28.Ng7+ Kd7 29.Qxf7+ Kc6 30.Nxe6 Kb6 31.Nc5 Rb8 32.Qxd5 1-0
[Site "Holguin"]
[Date "1989.05.22"]
[White "Sariego,Wilfredo"]
[Black "Borges Mateos,Juan"]
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 Bb4 5.e5 h6 6.Bd2 Bxc3 7.bxc3 Ne4 8.Qg4 Kf8 9.h4 b6 10.Bd3 Nxd2 11.Kxd2 Ba6 12.Rh3 Bxd3 13.Rxd3 Nc6 14.Rf3 Qd7 15.Ne2 Ne7 16.Nf4 Nf5 17.Nh5 Rg8 18.Ng3 Ne7 19.Qh5 Nc6 20.Ne2 Ke8 21.Nf4 Nd8 22.g4 Qe7 23.Rg1 Kd7 24.g5 g6 25.Qxh6 Nc6 26.h5 Rh8 27.Qg7 Rag8 28.Qf6 gxh5 29.g6 fxg6 30.Nxg6 Qe8 31.Rg5 Qd8 32.Qf7+ Kc8 33.Qxe6+ Kb7 34.Rf6 Na5 35.Nxh8 Rxg5 36.Nf7 Qg8 37.Qxd5+ Kb8 38.Qd8+ 1-0
[Site "France"]
[Date "1993.??.??"]
[White "Ballester,A"]
[Black "Seydoux,Harry"]
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 Bb4 5.e5 h6 6.Bd2 Bxc3 7.bxc3 Ne4 8.Qg4 Kf8 9.h4 b6 10.Bd3 Nxd2 11.Kxd2 Ba6 12.Bxa6 Nxa6 13.Rh3 c5 14.Rf3 Qe7 15.Nh3 Kg8 16.Rg3 Rh7 17.Rb1 Rc8 18.Nf4 Nc7 19.a4 Qd7 20.dxc5 bxc5 21.Rb7 Qc6 22.Rxa7 Qb6 23.Nh5 Kh8 24.Qf4 Qxa7 25.Qxf7 Rg8 26.Nf4 1-0
[Site "IECC email"]
[Date "2000.??.??"]
[White "Vujanovic,Aleksandar"]
[Black "Kamaluddin,Yusof"]
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 Bb4 5.e5 h6 6.Bd2 Bxc3 7.bxc3 Ne4 8.Qg4 Kf8 9.h4 b6 10.Bd3 Nxd2 11.Kxd2 Ba6 12.Rh3 Bxd3 13.Rxd3 Nd7 14.Rf3 Qe7 15.Nh3 Kg8 16.Nf4 Rh7
17.Nh5 Qa3 18.Rh1 c5 19.Rhh3 g6 20.Rxf7 Kxf7 21.Rf3+ Ke7 22.Qxg6 Nf8 23.Qg8 cxd4 24.Nf6 dxc3+ 25.Rxc3 Qb4 26.Nxh7 Qd4+ 27.Kc1 Qxe5 28.Re3 Qa1+ 29.Kd2 Qd4+ 30.Ke1 Qa1+ 31.Ke2 Rc8 32.Kf3 Kd6 33.Kg3 1-0
[Site "Mondariz"]
[Date "2002.12.15"]
[White "Serra Olives,Tomas"]
[Black "Borges Mateos,Juan"]
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.Bg5 Bb4 5.e5 h6 6.Bd2 Bxc3 7.bxc3 Ne4 8.Qg4 Kf8 9.Bd3 Nxd2 10.Kxd2 b6 11.h4 Ba6 12.Rh3 Bxd3 13.Rxd3 Nc6 14.Rf3 Qd7 15.Ne2 Ne7 16.Qf4 Ng6 17.Qg4 Kg8 18.Ng3 Qe7 19.Rh1 c5 20.Nh5 cxd4 21.cxd4 Qb4+ 22.Kc1 Rh7 23.Nf6+ gxf6 24.h5 f5 25.Qg3 Kg7 26.hxg6 fxg6 27.Qh4 Qf8 28.Rc3 g5 29.Rc7+ Kg8 30.Qxg5+ hxg5 31.Rcxh7 Qa3+ 32.Kd2 Rf8 33.Rh8+ Kf7 34.R8h7+ Ke8 35.Rb7 Qa5+ 36.Kc1 Qc3 37.Rhh7 Qa1+ 38.Kd2 Qxd4+ 39.Kc1 Qxe5 40.Rxa7 Qb8
41.Kb1 Qxa7 42.Rxa7 Rf7 43.Ra8+ Ke7 44.Rb8 Kd6 45.Rxb6+ Ke5 46.Kb2 Rh7 47.a4 g4 48.g3 Rh2 49.a5 Rxf2 50.a6 f4 51.a7 fxg3 52.a8=Q g2 53.Qb8+ Kd4 54.Rb4+Ke3 55.Qg3+ Ke2 56.Qxg4+ Ke1 57.Kc3 Re2 1-0