Probably not. After all, white hasn't done anything wrong that would deserve a punishment. I'm sure French players would have more insight on this, but I think it's just something you have to deal with if you play the French. Otherwise you can switch to the Caro-Kann, where the exchange variation is more interesting.
French Defence Exchange

Black can certainly get attacking chances by breaking the symmetry, eg castling queenside if White castles kingside (or vice versa). The drawishness of the Exchange variation is much overrated by club players - there are plenty of chances for both sides to attack, or to go wrong.

Sure black can create something. Like this :

The Exchange Variation requires patience and very strong positional understanding. For example, a line I get a lot and almost always win against is the following:
You can't force positions that fit to a cookie cutter mold. There are games where the best idea is to attack and there are others where maneuvering is the answer. The French Exchange is the latter. No opening has 100% scenarios of any type. I've seen tactical Slavs, positional Najdorfs, etc. The Exchange is a positional line in the French, but not a good one for White as, unlike say, the Four Knights Game, there is no issue with mimicking. In the Four Knights Game, there are tactical issues in many lines if Black merely mimics. So the key here in the Exchange French is to correctly determine when White has imploded (i.e. 11.h3) and take advantage of his error. In every game I play against the exchange (Slow Time Control, over the board - 5-minute cr*p on chess.com means nothing), White is the one fighting for the draw!
Playing aggressive involves going for c5, trading structure for initiative, not objectively best, but the best way to be aggressive in that opening. If you don't want to play it, you are basically out of luck. If you are not already tho, I would recommend this general move order/system:bd6, ne7, 0-0, bf5, nd7. Most players at a weaker level go for nf3/nf6 set ups, which from my experience are marginally worse.

The reason it's considered drawish is the open e-file. In positions with a single open file early in the game, the tendency is to trade off the Rooks & even Queens when they oppose each other. To avoid this, one can only avoid exchanging the major pieces. Minimize the power of the open file by making sure the opponent has no good entry points on your side of the board. If he gets a Knight established, supported by a Rook, you may be in some trouble.
Are there some aggressive lines for black in the French Defence when white goes for the exchange variation?