It's true that I considered 6.c3 only after 5.Bb2 (mistakenly adding dots as if they were Black moves, by the way). With 5.c3, White does gain the possibility of taking the e-pawn by chasing the Black Nc6 away with b5.
1.d4 c5 2.b4 cxd4 3.Nf3 e5 4.a3 Nc6 5.c3 d5. If White tries it, though, he will regret it: 6.b5?! Na5 7.Nxe5 dxc3 and 8.Qa4 (8.b6 is similar: Nc6 9.Qa4+ Bd7 10.Nxd7 axb6! and 11..bxc6), Bc5 9.b6+ Nc6 10.Nxc6 Qd7! with a typical pin motif, gaining time to retain the gambit pawn (11.Nxc3 bxc6 and ...Bxb6).
White really must use a somewhat insipid queen check from a4 in this line, otherwise Black develops a huge initiative--one way is with ...d4 and Be6, sometimes in conjunction with ...Rc8. For example, 8.Nxc3? d4 and Black must grovel with 9.Nb1 (not 9.Na4?? Be6 threatening both Bb3, forking queen and knight, and Nb3 followed by ...Qa5+, forking king and knight; nor 9.Ne4?? Qd5 forking the knights). Or 8.Bf4? g5 (planning ...Bg7) 9. Bg3 d4 10.e3 Be6 11.exd4 Rc8 -+.
Instead of trying to win the e-pawn by kicking the Nc6, just 6 cxd4 is a better try for White; I would consider this the main line. But Black retains a big advantage with 6...e4!, giving back the pawn for a superior reversed-French center. In the real French, the French side has exceptional piece coordination, but here the opposite is the case. After 7.Ne5, Black keeps more central piece control with normal development: simply 7...Bd6 8.Nxc6 bxc6 9.e3 (or 9.Nc3 Ne7), when Black can choose between 9...Ne7 heading for f5 and 9...Qg5 (in typical anti-French fashion), keeps the upper hand.
Perhaps even stronger after 7.Ne5 in the above line is the immediate minority attack 7...a5, but there's no need to mess with it; it's much more complicated and White has three or four equally good (bad) continuations.
All these lines issue in a rather large opening advantage for Black.
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