I have finally got around to covering all of the main variations of the Alekhine-Chatard Attack against the French Defence.
My opinion of the accepted lines of the gambit (6...Bxg5 7.hxg5 Qxg5) have changed quite a lot since examining the lines more closely. I don't think the old main line, played by Alexander Alekhine against Fahrni, Mannheim 1914, with 8.Nh3 Qe7 9.Nf4, is very convincing. I think Black can get quite a solid position with 9...Nc6 followed by ...g6, ...Nb6, ...Bd7 and ...0-0-0. The move-order is quite important; if 9...g6 at once, then 10.Bd3 is quite dangerous for Black, threatening sacrifices on g6. The lines with White sacrificing a knight on d5 after 10.Qg4 Nxd4 can easily burn out to a draw. At club level most players won't play accurately, of course, but even so, I am not sure about White's practical chances.
But I believe that 9.Qg4 looks quite promising for White, attacking g7 immediately and planning to follow up with Nf3-g5 in most cases. 8.Nb5!?, which has been discussed briefly at the Chesspublishing.com and also mentioned by John Watson, also looks quite promising. The modern move 8.Qd3 aims for long-term positional compensation rather than a quick attack, but also appears to give White at least sufficient compensation for the sacrificed pawn. The compensation persists even if Black engineers a queen trade with 8...Qg6 9.Qxg6 fxg6 (White can also consider 9.Qd2).
One common motif in the declined variations is that Black wants to get in ...c7-c5, undermining White's d4-pawn, without allowing White to get in Nc3-b5-d6. Thus, ...a6 is often played, but I don't trust the immediate 6...a6 7.Qg4 for Black, despite its popularity. 6...c5 7.Bxe7 leaves Black with a choice between 7...Qxe7 8.Nb5, often involving an exchange sacrifice on a8, and 7...Kxe7, which gives up castling rights but aims for long-term queenside counterplay. I think the 6...c5 line is better for White, but Black is not without chances.
Black's best declining moves are 6...Nc6 (which leads to positions with just a slight edge for White, and chances for both sides), 6...0-0, and 6...h6. The last two give Black good chances of theoretical equality, though White often gets a slight "pull" in the middlegame. In both cases, the positions tend to be double-edged with the kings castled on opposite sides of the board.
John Watson has recently written about some of these lines at Chesspublishing (though to see his full analysis requires a subscription). In his latest update he says 6...h6 "seems to be more reliable than the others" and gives 7.Be3 an exclamation mark, rather than the exchange of bishops with 7.Bxe7. He is a stronger player than I, but my investigations suggest that there is a strong case for his position.
I suspect that the Alekhine-Chatard with 6.h4 is not as likely to give White a theoretical advantage with best play as the standard 6.Bxe7, but it is a decent try for advantage, as well as increasing the payoff if Black goes wrong- White can sometimes pull off a quick attack and win very quickly.