I love playing Nc5 on the second move.
But seriously, I don't think it's named. e5 doesn't look good, you're committing the pawn advance without making black concede something. I'd play Nf3 or c4. With c4, the game can turn into a very weird NID. or something strange.
Yeah it has a name...illegal. But I doubt white would complain that black made an illegal move as he could just take the piece.
The Oxford Companion to Chess by David Hooper & Kenneth Whyld, 1984 lists 700 openings and variations in its Index of Named Openings and Variations, and doesn't list 2...Nc6 in the FD.
Nimzovitch used to play (as Black) 1.e4 e6 2.d4 d5 3.Nc3 Nc6 as a form of "odds giving" to weaker opponents, so I suppose you could call 2...Nc6 the Hyper-Accelerated Nimzovitch Odds-Giving Variation.
1.e4 e6 2.d4 d5 3.Nc3 Nc6 is actually not that bad. 4.e5 Nge7 is probably OK for black, and on 4.Nf3 Nf6 5.e5 Ne4 6.Bd3 there is quite a bit of established theory- white is just slightly better.
As played, I think black is very comfortable after 3.e5?! d6.
I'm pretty sure whatever the name, it's not a variant of the French defense.
No, actually 3.Nf3 is better using that move order, since 3...d5 can be simply answered by 4.e5, when the Nc6 is on the way of the c7-pawn, while the Nc3 is not. This French Advance variation should be surely enough at least slightly better for White. 1.e4 e6 2.d4 d5 3.Nc3 Nc6, or 3.Nd2 Nc6 (AKA the Guimard variation) are more logical. White is probably a bit better after both 3.Nc3 Nc6 as well as 3.Nd2 Nc6, but the road to the advantage is neither obvious, nor straightforward.
I saw an odd variation of the French Defense today and was wondering if it has a name and what the strategy behind it is or if it's just meant to throw main lines out the window and surprise an opponent.