French :: exchange variation - but not quite I had the following in a game



  [FEN ""]
1. e4 e6 2. Nf3 d5 



expecting White to follow with Nc3 leading to the Two Knight's Variation of the French

Instead, the game continuing with:



  [FEN ""]
1. e4 e6 2. Nf3 d5 3.exd5 exd5 4.d4





transposing, I guess to some form of the exchange variation although the typical  "exchange variation" happens in the French's main line: 1. e4 e6 2. d4 d5. Anyhow, is there a name for this opening and how should Black continue? (e.g. with 4....Bb4+ maybe?). Alternatively, might there be any merit in the adventurous 3...Qxd5 which loses a tempo for Black if followed by 4.Nc3?
The game has transposed to a standard exchange variation, a variation pretty well explained on Wikipedia.
You could try a setup with 4... Bd6, 5... Ne7, with the idea that if white puts his best  bishop on Bd3, you can play Bf5 to change it off. Black is very comfortable.

The move 4... Bb4+ is not to be recommended, since it only helps white, giving them the free move 5.c3.

3...Qxd5 should be avoided since in the Scandinavian positions that arise, it is important to develop the c8 bishop before playing e6.