More on the Anti-French Line - and a New Question
Rick Kennedy's comment addresses some of the divergences between the work I've independently done (some of which I've presented here) and that of the gambit's originator, Stefan Bücker. For instance, after 4...Nf6, I considered and played 5.e5 for a while before moving on to 5.Nc3, but Bücker (at least in 1983) was advocating 5.e5 Ne4 6.Nf3. Second, in the gambit accepted with 4...dxe4 5.Bc4 Qe7 6.Nc3 Nf6 7.d3 exd3+, Bücker prefers 8.Be3 to the 8.Kf1 advocated in my initial Anti-French post.
Bucker is right on both counts, although I'm ambivalent about the first case, as the positions after 4...Nf6 5.e5 Ne4 6.Nf3 are rather flat and allow Black several ways to keep the balance. (For problems with 5.Nc3, see Dragon's comment here. My view is that unless Black is a strong player who has worked things out in advance with the computer, White has nothing to fear, but the chess truth is in Black's favor there, as far as I can tell.)
The second case is more interesting and entertaining. Dragon's line, which I also discovered some time ago as well (as did Bücker, I'm sure), refutes 8.Kf1, but 8.Be3 is more robust. Ironically, when I was figuring out the line for myself, years ago, 8.Be3 was the first move I came up with, but since 8...d2+ in reply can force the king to move anyway and I'd rather have the bishop on g5, I moved on to 8.Kf1.
It turns out that 8...d2+ isn't such a big deal, but Black can get an edge if he threads the needle very carefully: 9.Kxd2 Nc6! 10.Re1 Ne5! 11.Bf1 (not the most forceful move, obviously, but allowing 12...Nxc4+ 13.Qxc4 Be6 gives Black an easier life) Qd6!
(11...c6 is less clear: 12.Bd4 Nfg4 (12...Be6 13.Rxe5 Bxb3 14.Rxe7+ Bxe7 15.Bxf6 Rd8+ 16.Kc1 Bxf6 17.axb3 is similar) 13.Bxe5 Nxe5 14.f4 Be6 15.Rxe5 O-O-O+ 16.Kb1 Bxb3 17.Rxe7+ Bxe7 18.axb3 results in an imbalanced ending which is probably slightly in Black's favor, but it's not unusual to find the two minors coming into their own against the rook.)
12.Kc1 Be7 13.Nb5 Qc6+ 14.Qc3 Qxc3+ 15.bxc3 and now Nd5 gives Black some pull, though I believe White can hold.
In sum, the improvements are there for Black, but finding them OTB is an arduous task, and in most cases White's disadvantage is at worst a slight one.
Here's a new question (discuss amongst yourselves...I'll give you a topic): is it somehow improper to play such variations; that is, to play a line one knows to be unsound? Reasons one might think so include disrespecting the game, disrespecting one's opponent, placing competitive ends over the sorts of noble motives like self-improvement and creating beauty one might think necessary to ethically justify playing chess, etc.