I don't know from were you study the French , but what I see on the diagram it's generally not favorable for white. White doesn't like so early the exchange variation exd5 in the French . It simplifying the center, it open the diagonal for blacks bishop to develop easy! when in other variations blacks main problem is what to do with the light sq bishop.
White face difficulties to prove an advantage over the exchange variation. After 3...c5 play 4.Nf3 , the Tarrasch variation is more flexible system were white has some chances to prove a better position in the middle game.
I'm studying the French Defense for white and was suprised by this line where it's recommended to throw in an early check and I guess hopefully trade light bishops. I was wondering what the purpose is. I get that Black has the IQP but even with that stockfish isn't giving white that much of a advantage. What does white get out of trading bishops this early?
Edit: 5.Nf3 before Bb5+!