c. None of the above
Qe2+ or Qe7+

c. None of the above
That doesn't seem to help. Maybe lines where Qe2+ is actually good would be a little more helpful.
I do see an error in the "main line" of the first since it should be 10... Rxe3, 11. fxe3 Qxe3.

I don't think it's so good in the first diagram, and I think black responded correctly. After that neither side played very well. 7. Bxe7 wins for white.

I don't think it's so good in the first diagram, and I think black responded correctly. After that neither side played very well. 7. Bxe7 wins for white.
So it looks like 6... Nf6 would be needed, or maybe this is why Nc6 would be better than Nh5. This means that O-O-O stops the pin, unless black moves the knight and white deicdes to leave their bishop there since it is technically defended by the knight. By the way, they're not really games, except for the variation that starts 5. b3.

Just to give you a bit of an idea of the setup.
You can also castle kingside too and trade off the light squared bishop with ...Bf5 but its to give you an idea of the development. Most white players relax because the exchange is 'drawish' for GMs yes for the rest of us not so much. Uhlmann has a great conversation about the exchange in his book "winning with the french, I strongly recommend the book just to learn how to appoach the french as a whole.

e4 e6 d4 d5 exd5 exd5 nf3 bg4?! Qe2+! Qe7 Be3) and queenside castle for white, rarely is something like this good, one of the few cases where its okay
I wish you could have at least put turn numbers. I see that in this example white doesn't rush for the queen exchange.

Just to give you a bit of an idea of the setup.
You can also castle kingside too and trade off the light squared bishop with ...Bf5 but its to give you an idea of the development. Most white players relax because the exchange is 'drawish' for GMs yes for the rest of us not so much. Uhlmann has a great conversation about the exchange in his book "winning with the french, I strongly recommend the book just to learn how to appoach the french as a whole.
Thanks for the games. I'm actually asking about 4. Qe2+, not about the exchange variation in general, although I should read more about it since it seems to be done 90% of the time at my level. In these games the players don't even bother with it, which seems to reinforce my thoughts that it isn't the best move.

again why look at a variation thats just subpar for black? why not Bd6? if 4. Qe2+ Ne2 and white is going to be in trouble down one tempo in a symmetrical position can be a big problem

Do you mean 4. Qe2+ Ne7? In my limited experience, Ne7 really sucks. It completely blocks the bishop in. I haven't tried Be6, at least I don't think so.

Why didn't Black capture the queen at all?
When do you mean?
On move 9 in ur first diagram.
You could have played Rxe2 instead of Qxg5
And after on move 10, Instead of Qxe3+, why not Rxe3?

pay attention clavier. In the line I am talking about and the games mentioned ...Bd6 is played first so the bishop isnt blocked

The only real point in that sort of move is to prevent your opponent from castling. In general, by that point, you have enough of a developmental advantage to easily win the game.
To give credit where credit is due, I found this example in Silman's excellent book How to Reassess Your Chess, 4th edition.

Why didn't Black capture the queen at all?
When do you mean?
On move 9 in ur first diagram.
You could have played Rxe2 instead of Qxg5
And after on move 10, Instead of Qxe3+, why not Rxe3?
I did say in post #4 that 10. Qxe3+ is wrong since Rxe3 is better. 9... Qxg5 is better than Rxe2 because it gains a knight and gives check, meaning the queen is still free to take next turn. All white could do is 10. Kb1, 10. f4? (10... Qxf4+, giving black an extra pawn), and 10. Qe2.
As for TonyH, I see your line is fine, but I see 4. Qe2+ the most often, meaning 4... Bd6 is not an option. I'm not asking about the exchange variation of the French when played against someone better than I, but against those who love to rush into queen exchanges, or their queen is the first piece moved after their pawns. When I was at 700 I saw a lot of people moving their queens as soon as possible and I still see it now that I'm almost 1200. At least I haven't seen the center game in a while.
ChessisGood, that is an interesting game, but as you point out, it's well developed and not 4. Qe2+.

OK i think i see what your aimming at. Your observation is very accurate. I have seen a lot of beginners trade pieces for no reason , use one move threats or 'flash' attacks with 1 or 2 pieces to win. The best policy to beat these types of players is use each tempo to gain ground slowly then open the position. They usually will continue with their random moves and make progressive mistakes that accumulate into more problems than they can manage. I found this game between a 2145 and 2430 player. the logic of what i Mentioned above I think is shown here really nicely. (Actually a good teaching game IMO never seen it before but I like it)

When I see this game, I wonder "Why 22. Qh5?" Well, I also wonder about 8. Ne5, 10 Nd3, 13. Bh3, and other things. With 22. Qh5, I just wonder "Why not Qxc6? This looks like one of those games white won for black.
I always felt it was silly to do waste an active piece to take an equal, inactive piece. Here is the full game where white played 4. Qe2+, but they also do some weird thing with their bishop and then ignore the queen pin. I'm interested to see what you think of it.
It's interesting that I make 4 pawn moves total and they make 10.
Is this ever a good move? I think that moving the queen quickly later would be best, but then it seems like it might be a wasteful move. To me it seems to risk having the queen pinned and blocks in the king's bishop. I don't know how many times I've seen this and then watched the enemy keep the queen there while they continue their development.
P.S. I think they're going for this, but I always have bad luck with this and always move the bishop to answer the check. Using the knight really sucks.