This was a loss, but a very crazy one.

Nice game.  I feel sorry for you.  Usually I don't play against opponents so much stronger then me (at least in rated games). 

2...Nf6?! Is just a silly transposition into the Alekhine. Maybe it is just personal, but I find the Alekhine much easier to play against than the French so I think 3.E5 is a good move.

4. e5 Hmmm.. I don't think this is good. As you found in your game, it is necessary for the pawn to be on c3 to defend d4 in the Advanced French. Sure, you make the knight retreat here, but you have to think of the long term effects.

5.Bd3 This isn't bad. You're going to have to play Nf3-e2 to defend the d pawn, and then you can play c3 and reposition the knight to f4 or g3.

7.Bb5? A bad plan, as you found out in the game. Besides that, you're moving your bishop two times in the opening. This is rarely useful.

You could use some more planning. If you looked ahead to black's possible moves, you could have found some of your mistakes.

If I played 7. Ne2, he could win my e5 pawn though, with ...cxd4 Bxd4 Nxe5.

Edit: Also, he could play ...c4, trapping my bishop.

Of course, my mistake. x.x Well, in that case, Bd3 was probably bad. Maybe you should have delayed moving your bishop with 5.Nce2, then c3 and Ng3 and finally developing your bishop to e2. I know I'm contridicting myself there, but it seems like it's the only way besides moving your bishop to b5 and letting it get chased around. Be2 right away will badly tie your pieces down to d4.

A bit of opening advice:

2... Nf6 allows a transposition to a dubious variation of alekhines defense by e5.  Follow up moves GENERALLY include d5, c5, Nc3, and f4.

4. e5 is a perfectly sound move.  Something had to be done to relieve the pressure on e4.  The best alternative was Bg5 pinning the knight, exd5 Is objectively bad because it gives white no advantage (although some prefer the open lines of the exchange variation subjectively)

5. Bd3? is bad, but not as bad as you think since this move would be played anyways.  It did endanger your c5 pawn by blocking the queens path to it, but don't feel ashamed of this move, lesson learned!  Best is actually 5. f4! so Nf3 can be played without blocking in the pawn.  f4-g4-f5 can be used for counterplay later.

7. Bb5 probably shouldn't have been played.  I personally would have played Nf3 and dxc5 to cut my losses, as Bb5 lagged in development even further and traded good bishop for knight.

8. a4? was a waste of time.  Bxc6 was nessecary.

And of course as you noticed Kd2? was a mistake.  After that, the game just got rediculous...

Since you have appearantly never seen the french defense before, you did well for your first time!  Don't feel too down!

Heres what I play.  I forgot to mention 3... Bb4 (an immensly popular variation) so be sure to read up on that as well.