Why did you play 3...c5? To attack the d4 pawn. What is the typical response? 4.c3 so that White can recapture in the centre with a pawn. Did he play the virtually forced c3 so that he could take back with a pawn? No. So why didn't you play 4...cxd4?
Think about why you're playing the moves you're making.
But after ..cxd4 he can play Qxd4 and has Queen stationed in the middle....no?
As often happens with queen's early in the middle, can attack it with nc6, and bump it away.
b6 was terrible as was Nxd7 which allowed the destruction of the Black Q-side.
The French Advance is about pawn chains. 4cxd4 means that White's pawn on e5 is going to be harder to defend as it can no longer be defended by d4. If 5Qd4 then 5Nc6 attacking the weak e-pawn and the Queen.
Everyone above is correct, but your position wasnt that bad until you dropped a pawn with 8. ...nxd7. You need to ask yourself what 9. ... f5 was intended to accomplish, because that was terrible too. Leaving aside what actually happened, f5 doesnt develop anything. 9. ... ne7 followed by 10. ... g6 and you finish your development.
The french defense is an advanced defense not suitable for beginners or advanced beginners. The level your at, many GMs recommend playing E5 in response to E4 and simply trying to develop rapidly. If you want to learn a specific defense, there are others that are easier on beginners, such as the caro kann. Again though, you didnt really lose because you played the French or because you botched the opening, rather you lost because you dropped a pawn and then made it worse by a weakening pawn move (f5) when you should have been developing. After that, your position is wretched anyway, and dropping your rook was almost a mercy because it made the position resignable.
But after ..cxd4 he can play Qxd4 and has Queen stationed in the middle....no?
No.
The Advance French is an "ideas" opening. Until you get familiar with the ideas it will be a problem. But as a life-long French player I love to see it, because Black gets to express a bunch of French-y ideas (attack on the base of the pawn chain, attack on the head of the pawn chain, central pressure from the wings) in very pure form.
The basic issue is that White has put that pawn center out there. If you leave it alone it will crush you: White has more space and the pawn center points toward the kingside, meaning a probable kingside attack.
However, White's taken on a big responsibility to keep that center intact, and it is not easy to do. Black can pressure the base at d4 by ...c5, ...Nc6, ...Qb6, ...Nf5 (via e7 or h6). If White trades it off the center is just a pawn on e5 which can be pressured by the knights or traded off by ...f6. Then it's Black who has center pawns ready to roll. If White doesn't trade and instead supports with c3, Black will trade and then pile on the d-pawn. White can defend it with correct moves, but it's easy for him to lose the initiative and get forced into a defensive posture. Black can hardly ask for more in the opening.
In my experience, against weaker players Black often just wins a pawn (d-pawn or b-pawn, sometimes even f-pawn). A strong player can make White's center work, but it's a tricky juggling act: a lot of "sensible developing moves" lead to the collapse of the center, after which Black is better.
People will tell you that beginners "have to" play 1...e5 but really you can play whatever you want! It'll just take some time to get familiar with the plans in your opening of choice.
Here's one way to check out where you went wrong yourself and hopefully remember it so it doesn't happen again.
First go to a position that looks ugly for Black.
14. Qxa8, you're probably busted, so problem happened before then.
Say 9. Qxd5. It may be holdable for Black but probably won't be much fun. Black problems: down a pawn, qside busted up, going to take a long time for king safety if possible at all. Black's plusses???
So you know something probably went wrong before then. How about at 7. Bb5+? Black ok on material. Has hanging c&d pawns. A weakness? Maybe not now but could be a problem. King safety not great and current check irritating. Problem could come as check block leaves d5 unprotected. A plus for Black is that White's only has one developed piece. Overall, Black probably not equal but likely playable.
So now you put the position 7.Bb5+ on the board and go over it with another player or computer and try different variations so that at move 9. you're hopefully better than you were at 9. Qxd5.
You might also want to try the same on the board analysis for earlier, where you got surprised in the opening which I'm guessing was 4.c4 which is not a simple position. Try different variations and you'll come up with one that suits you there too. Or you might be OK with getting to 7. Bb5+ if you found a decent continuation from there.
If you like the French, keep playing it with some study and if you also do this kind of game self review, you won't end up being negatively surprised very often.
So I tried out the French Defense for the first time and of course, my opponent suprised me with the advanced variation. I know I went wrong somewhere early on with the pawns and once his white queen was out I knew I'd done something wrong. Any ideas? I'm black of course.