The French defense is a popular response to 1.e4
a typical game would continue 1.e4 e6 2.d4 d5 and from here there are 4 main continuations.
The first is the exchange variation where white plays 3.exd5 and the position is considered about equal.(The second variation is shown above)
The second variation is the advance variation which usually goes 3.e5 c5 4.c3 Nc6 5.Nf3 Qb6 then there is a choice between a3, Be2, and Bd3. Euwe's move, 5...Bd7, is also popular.
The third variation is the Tarrasch in which white plays Nd2 then black mainly responds with 3...c5 or 3...Nf6, or the Guimard varation, 3...Nc6.
The fourth variation is 3.Nc3. There are many variations leading from here including the Winawer, the Rubinstein, the Classical system, and 4.Bg5.
The downside for black in the French is that Black's light square bishop is very inactive.