What are the ideas for White in the Monte Carlo (French Defense)?

According to chessgames, Rapport played the French Exchange 5 times. Do you know his score? 4.5

Not so bad for a "junk" opening, don´t you think?

One thing that all 3 losses have in common for Black.  They all involved Black playing ...Nc6.

I don't advocate that idea at all for Black.  Black should not be the one trying to break the symmetry IMHO.  As Black, I make White make the first committal move.  Given the exchange of pawns on d5, the d5-pawn is not moving any time soon, and Bb5 is garbage because of ...c6, and Be2 is super-passive, and so the Bishop almost automatically wants to go to d3.  The King's Knight almost always goes to f3, occasionally e2.  The queenside pieces have more diverse options.

Therefore, I consider Bd3, Nf3, and c3 "Non-Committal" moves, and will mimic them when played, forcing White to show his hand first.  Once White starts developing his Queenside pieces, that's when I start to deviate, and as I see it, a pawn belongs on c6, not a Knight.

I actually just wrote an article this morning on an Exchange French game that I just finished in what is basically the Email Correspondence Championship in the United States (Semi-Final Round of the 2017 Electronic Knights).  It can be found here:

https://charlottechesscenter.blogspot.com/2019/06/the-french-connection-volume-21.html

You will see that White commits the DSB early while I play the non-committal moves ...Bd6, ...Nf6, and ...c6 - once again, NOT putting the Knight there!

Admittedly, I made one crucial error on move 29, but White failed to capitalize, and I won in 53 moves.

Once again, you have to look at why he scored 4.5 out of 5 and not just blindly say that because he scored 4.5 out of 5, the Exchange must be great.

As long as White's moves are non-committal, I say the answer is mimic.  I have many times had the position after 1.e4 e6 2.d4 d5 3.exd5 exd5 4.Bd3 Bd6 5.Nf3 Nf6 6.O-O O-O 7.Bg5 Bg4 8.Nbd2 Nbd7 9.c3 c6 10.Qc2 Qc7 and it's here that typically White ends up having to commit first.  I often get the following:

• 11.h3 - I then play 11...Bh5 and do not play h6.  This allows me to play ...Bg6 and contest the diagonal.  Even if the Knight goes to h4 and the Knight takes on g6, the g6-f7-g7 setup is sufficient to block White's battery.
• 11.Rae1 or 11.Rfe1 - I will often counter with the opposite Rook, breaking the symmetry there
• 11.b4 or 11.a4 - Often Queenside play by White I will counter with bringing the Rooks to the e-file and countering on the Kingside.

I view this as basically nothing for White.  Lower rated players will fail the equal middlegame and lose anyway.  If a 2400 player want to play like this, and actually plays this position correctly, and wants to give me a draw - I have no objection!  A draw with Black against a 2400 player?  Yes, Please!

The Queen’s Gambit is a gambit - sacrificing a pawn for a lead in development that in the middlegame will convert into a crushing attack that wins the game, either by a checkmate or by big material gains out of the attack into a winning endgame where the gambit player wins easily. And the Monte Carlo is a “version” of the queen’s gambit, also aggressive and this is an example where white wins.

A gambit is an aggressive opening where one gives up a pawn to get a lead in development and in the Middlegame turns the better position into a strong, often winning attack where pieces get sacrificed and the enemy king checkmated in the end of it all. The Queen’s Gambit is a very clear example of a gambit - sacrificing a c-pawn. The Panov is a version of the Queen’s Gambit in which White’s e-pawn and black’s c-pawn are gone. The Monte Carlo is another Queen’s Gambit - just with the e-pawns gone. So the Monte Carlo is an aggressive response to the otherwise positional French Defense, just like the Panov is an aggressive response against the Caro.

A gambit is an aggressive opening where one gives up a pawn to get a lead in development and in the Middlegame turns the better position into a strong, often winning attack where pieces get sacrificed and the enemy king checkmated in the end of it all. The Queen’s Gambit is a very clear example of a gambit - sacrificing a c-pawn. The Panov is a version of the Queen’s Gambit in which White’s e-pawn and black’s c-pawn are gone. The Monte Carlo is another Queen’s Gambit - just with the e-pawns gone. So the Monte Carlo is an aggressive response to the otherwise positional French Defense, just like the Panov is an aggressive response against the Caro.
Queen’s Gambit versions: