The synopsis was incorrect. There was nothing to indicate that Louise was the doctor's daughter. The commentary booklet with the DVD refers to her as a kind of surrogate wife and mother. I updated the synopsis.

In the synopsis, it read, "The woman is Louise (Alida Valli) and her father Prof. Genessier (Pierre Brasseur) has been attempting to perfect a number of surgical procedures". So this implies the doctor has two daughters, but where in the movie did it say that Louise is his other daughter? I just watched it and there was no mention of what her relationship is with him except that he helped repair her face.

Early in the film the police describe Louisa as a foreigner. Later in teh film the doctor provides advice to Christiane on how she might return to the world post-transplant and he talks about her travelling and returning with a new identity. I think the two scenes are linked and suggest that Louisa might be his wife. The film never decides so it's up to each viewer as to how they view Louisa and her actions.
Keep silent unless what you are going to say is more important than silence.

I could be wrong (and the film isn't entirely clear), but my impression was that the assistant got a new face (actually, just got her old face fixed up with plastic surgery, with no transplant implied) some time ago (well before the accident), and became enamored of the doctor out of gratitude and admiration for his skills. I don't think she is necessarily his wife.