Although this position contains several common elements that arise in the French, it appears in only thirteen games in the ChessBase online database. It also cropped up in my second blitz game this morning.
The position arises in the Tarrasch after 1.e4 e6 2.d4 d5 3.Nd2 Nf6 4.e5 Nfd7 5.f4 c5 6.c3 Nc6 7.Ndf3 cxd4 8.cxd4 f6 9.Ne2 Bb4+ 10.Kf2 fxe5 11.fxe5 O-O*
White to move
My opponent played 12.Kg1 and I won the game in 47 moves. He lost a pawn on move 33 and lost a piece to a knight fork on move 44.
Black's immediate target is e5. If it were Black's move, the pawn could be taken as one of the defending knights is pinned. The locked center with targets on d4 and e6 is typical of the French Defense. White's king on f2 is a common maneuver. White's bishops have more scope even though neither has moved.
My opponent stepped out of the pin.
A) 12.Kg3 was played in three games. That was the end of one game--a draw was agreed. It was the only game between masters. 12...Ne7 and 12...Nb6 were played in the other two games.
12...Ndxe5+ has not been tried. 12.Kg3 might be regarded as an error.
B) 12.Be3 was played in three games. All continued 12...Ndxe5 13.dxe5 Nxe5
White to move
Skripchenko -- Maric, New Delhi 2000 continued 14.Qb3 b6 15.Rd1 Qe7 16.Kg1 and was drawn in 42 moves.
14.Bd4 was played in the other two games.
Black won a long battle in Matsura -- Cordova, Sao Paulo 2006 that continued 14...Nc6 15.a3 Bd6.
A draw was reached after a few moves in the more recent Kumaran -- Ram, Chennai 2013: 14...Qh4+ 15.Ng3 Nxf3 16.gxf3 e5 and drawn three moves later. 16...e5 may be inaccurate.
Black certainly has the better game after 12.Be3, which may be regarded as dubious at best.
C) 12.a3 was played in three games.
A correspondence game continued 12...Qh4+ 13.Kg1 Rxf3 14.gxf3 Ndxe5
White to move
White should have been happy to escape this correspondence game with a draw.
12...Ndxe5 was played in the other two games.
Black seems to have found frustration in Popov -- Danin, Smolensk 2005, which continued 13.dxe5 Bc5+ 14.Ke1! Nxe5 15.Nxe5 Bf2+ 16.Kd2 Qg5+ 17.Kc2 Qxe5 18.Kb1
Black to move
After his long journey, the White king appears less vulnerable and White went on to win.
White also survived Black's early attack in Polgar,J -- Hernandez, Merida 2000. That game continued 13.axb4 Qh4+ 14.Kg1 Nxf3+ 15.gxf3 Rxf3 16.Ng3 Nxd4 17.Bg2
Black to move
White went on to win.
Black should have the better game after 12.a3, but in practice has failed to prove it.
D) My opponent's 12.Kg1 may be an error.
However, I missed the thematic 12...Ndxe5. Instead, I tried 12...Qb6. My opponent played 13.Be3
Black to move
13...Ndxe5 remains the correct move. Instead, move-by-move, I squandered my advantage and won only due to tactical errors by my opponent in the ending.
Searching the database for the position in the first diagram produces games where it appears that White should be okay. With optimal play by both sides, however, Black should have a clear advantage. White's pawn center is weak in part due to the vulnerability of the White king.
*Notation leading to the diagram position was added per a request in the comments below.