if black would improve with such a trade then it must follow the bishop is weak...right?
I agree. Yet, my own experience has shown me that the French Bishop is not as weak as one might think. As an attacking piece, it is bad but as a defending piece, it is good.
In the French Defense... Blacks light square bishop, or "French Bishop", sitting on c8 gets a lot of bad rep. People say that that the French Bishop is a bad piece and that it is a weakness for Black because it has difficulty getting developed to an attacking square. However, in my experience, this bishop is an invaluable defensive piece in the French Defense and should not be underestimated. Often, the French Bishop can be the lynchpin that secures all of the light squares in your position. Plus, if White ever wants to trade bishop for bishop, then Black can only improve from such a trade. Your thoughts?