I always figured that being White in a French is a normal part of the repertoire of a Veresov player; I recall one accepting my invitation via 1. d4 Nf6 2. Nc3 d5 3. Bg5 e6 4. e4.

Here's a d pawn special where the frontiers of theory were reached after only five moves.

1. d4 Nf6 2. Nc3 d5 3. Bg5 c5 4. e4 dxe4 5. dxc5 Qa5

Move 4 alternatives for Black are 4. .. cxd4 and 4. .. Nxe4. In the latter, it is a known idea to play 5. Nxe4 dxe4 6. dxc5 Qa5

In the game line, 5. d5 was also possible, transposing as in the similar line of the Blackmar into something resembling a reverse Albin.

For what it's worth, the game continued (after 5. .. Qa5) with 6. Qd2 Nbd7 and now White elected to go for the ending with 7. Nxe4 Qxd2+ 8. Nxd2 Nxc5 . Presumably the ending has equal chances, but isn't automatically dead level because of the asymmetric pawn structures.

Games starting 1. d4 Nf6 2. Nc3 can be a problem for the second player. If you dislike defending a Pirc, that rules out 2. .. g6 and 2. .. d6 whilst the semi-Benoni that can arise after 2. .. c5 isn't marvellous either. French players would be happy enough to play an early .. e6. Otherwise you have to play 2. .. d5 and live with whatever they throw at you on move 3.