I disagree. After 1 d4 e6 2 e4 d5 3 Be3 dxe4 3 Nd2 Nf6 4 f3 Nd5 the correct move is 5 Qe2!

Really, I have played the Alapin-Diemer Gambit, and done quite well with it.

I don't think the French Defence is easy to "short-cut", since 3.Be3 dxe4 4.f3 (4.Nd2 Nf6 5.f3 is met by 5...Nd5) puts White at risk of ending up in a Blackmar-Diemer Gambit, Euwe Defence with the bishop placed on e3 rather than on g5. 

For the sort of double-edged attacking play that the typical BDG-er is after, I think 3.Nc3 is the way to go, but it does require some knowledge of relatively mainstream stuff in the French Defence.  3...Nf6 4.Bg5 dxe4 5.f3 exf3 6.Nxf3 is a straight transposition to the Euwe Defence, and 4...Be7 5.e5 Nfd7 6.h4 and 4...Bb4 5.e5 h6 6.Be3 Ne4 7.Qg4 both lead to double-edged play very quickly.  After 3...Bb4 I like 4.a3 Bxc3+ 5.bxc3 dxe4 6.Qg4 (I find the Winklemann-Reimer Gambit 6.f3 unattractive because of 6...c5, and 6...e5 is also good).  But of course those lines demand a bit of additional specialist knowledge of the main ideas for White.