I think you should be really lucky if so many people play the exchange...blacks position is already quite safe !? You can even try for more then the draw, look for example at Gurevich-Short, Manila 1990.
If i may copy-paste some text from the internet:
Exchange Variation: 3.exd5 exd5
The Exchange Variation was probably White's most popular response to the French in the 19th century, but has been in decline ever since. Garry Kasparov experimented with it in the early 1990s but later switched to 3.Nc3. Note that Black's game is made much easier as his queen's bishop has been liberated. It has a reputation giving immediate equality to Black, due to the symmetrical pawn structure. Many players who begin with 1. e4 complain that the French defense is the most difficult opening for them to play against due to the closed structure and unique strategies of the system. For example, Bobby Fischer was notoriously poor at playing against the French Defense. Thus, many players choose to play the exchange so that the position becomes simple and clearcut. White does not keep the advantage of the first move, White often chooses this line in hopes of an early draw, and indeed draws often occur if neither side breaks the symmetry. An extreme example was Capablanca–Maróczy, Lake Hopatcong 1926, which went: 4.Bd3 Bd6 5.Nf3 Nf6 6.0-0 0-0 7.Bg5 Bg4 8.Re1 Nbd7 9.Nbd2 c6 10.c3 Qc7 11.Qc2 Rfe8 12.Bh4 Bh5 13.Bg3 Bxg3 14.hxg3 Bg6 15.Rxe8+ Rxe8 16.Bxg6 hxg6 17.Re1 Rxe1+ 18.Nxe1 Ne8 19.Nd3 Nd6 20.Qb3 a6 21.Kf1 1/2-1/2 (the game can be watched here).
However, despite the symmetrical pawn structure, White cannot force a draw. An obsession with obtaining one sometimes results in embarrassment for White, as in Tatai-Korchnoi, Beer Sheva 1978, which continued 4.Bd3 c5!? 5.Nf3 Nc6 6.Qe2+ Be7 7.dxc5 Nf6 8.h3 O-O 9.O-O Bxc5 10.c3 Re8 11.Qc2 Qd6 12.Nbd2 Qg3 13.Bf5 Re2 14.Nd4 Nxd4 0-1. A less extreme example was Mikhail Gurevich-Short, Manila 1990 where White, a very strong Russian grandmaster, played openly for the draw but was ground down by Short in 42 moves.[2]
To create genuine winning chances, White will often play c2-c4 at some stage to put pressure on Black's d5-pawn. Black can give White an isolated queen's pawn by capturing on c4, but this gives White's pieces greater freedom, which may lead to attacking chances. This occurs in lines such as 3.exd5 exd5 4.c4 (played by GMs Normunds Miezis and Maurice Ashley) and 4.Nf3 Bd6 5.c4. Conversely, if White declines to do this, Black may play ...c7-c5 himself, e.g. 4.Bd3 c5. This idea was employed successfully by Korchnoi, but it is probably best to reserve this risky strategy for must-win situations.
If c2-c4 is not played, White and Black have two main piece setups. White may put his pieces on Nf3, Bd3, Bg5 (pinning the black knight), Nc3, Qd2 or the Queen's knight can go to d2 instead and White can support the center with c3 and perhaps play Qb3. Conversely, when the Queen's knight is on c3 the King's knight may go to e2 when the and the enemy Bishop and Knight can be kept out of the key squares e4 and g4 by f3. When the Knight is on c3 in the first and last of the above strategies, White may choose to castle on the Kingside or the Queenside. Obviously, opposite side castling leads to dynamic checkmate struggles and when the Kings castle on the same side the players usually putz around and don't do much until a complex endgame is obtained. Black may do the exact mirror image of all of the choices above. The positions are so symmetrical that the options and strategies are the same for both sides.
Another way to imbalance the game is for White or Black to castle on opposite sides of the board. An example of this is the line 4.Bd3 Nc6 5.c3 Bd6 6.Nf3 Bg4 7.0-0 Nge7 8.Re1 Qd7 9.Nbd2 0-0-0.
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