In the film, Maxime only learns that Hannah had "blundered" and presented the wrong document to the police - he never learns that she intentionally incriminated both herself and her son.
In the book, does Maxime ever learn the truth about what Hannah did?
No, he does not.
But never the less, you can see in the movie (book is more subtle, since you really can not convey emotions in a book as well as the actor can in his body language) that he knows that something is not right, that perhaps there was no blunder.
Also, it was explained that Maxime's "undoing" was learning that she gave up the identity of their son.
It seems he knew - even if indirectly. Hannah's action spoke volumes.
http://www.youtube.com/watch?v=rbhrz1-4hN4
In the context of the movie he would have not figured out she wanted the boy with her. Whether she made it out alive or not.
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