1. e4 e6 2. Bb5!? is the variation of the day.
This move does not refute the French Defense, but it’s an interesting surprise option. It’s certainly an awkward move. What benefit does this have for white? Well, first off, it develops a piece. And I suppose there is some sort of case to be made that it pins black’s d-pawn for now, although that hardly seems like an advantage, since black has quite a few ways to break this pin without compromising his position. But this is not an option that really forces any compensation from black.
2. … a6 might be a bit premature, but it does force white to make a decision about what to do with the bishop. 3. Ba4 is consistent but forces the bishop off the longer diagonal. 3. Be2 d5 can be compared with 1. e4 e6 2. Be2 d5 where the key difference is that black has committed to a6., but that may be slightly advantageous for black.
Of note in the original position is that moving this bishop leaves the g2 pawn unguarded. The bishop is also vulnerable to attack. This suggests the interesting 2. … Qg5!?
Obviously white cannot lose the bishop. He can either guard the bishop or move the bishop in this position. Possible moves for guarding the bishop are a4, c4, Na3, Nc3, and Qe2. Possible bishop moves are Ba4, Bc4, Bd3, Be2, and Bf1. White can also intercede with 3. e5?! but white loses a pawn and white gains nothing tangible in compensation.
Of moves that guard the bishop, only 3. Nc3 has any merit. 3. … Qxg2 4. Qf3 Qxf3 5. Nxf3 and white has a lead in development in compensation for the pawn, although black’s position is very solid and has quite a lot of flexibility. Black might consider b6 followed by Bb7.
Most interesting of white’s move options is 3. Bf1!? Returning the bishop to its original square is the only move that saves both the bishop and the g-pawn.
Black should now move the queen, since white will play either Nf3 or d4. Reasonable options are Qa5, Qg6, and the rather surprising Qd8!?, returning the the same position after move 1. Either Qa5 or Qg6 seem reasonable, with each of these having pros and cons.