How can they pay a Full prof 37k? That's for maitre de conf isn't it?
No it is for a tenured full prof (Professeur des universités), but which precise salary you get will depend on different things, including years of experience. A maitre de conférence is paid on a different scale (even lower).
You can see the scale here :
You see that depending on rank (which depends on years of experience either in academia, in an institution, in the industry if it is relevant to the position, either in France or abroad...), a Professeur des Universités gets paid from 3 125,58 € gross per month to 6 227,73 €.