having just seen this discussion again and seen Vero and Helens’ further replies, given I’m not French, but have been involved with the authorities in 4 Depts since 2001, have just reminded me, Yes it boils down to what the specific forms ask for 
nom du Naissance = your maiden name, which can be backed up by your birth certificate.
nom du marriage / nom d’usage / nom = Surname, both or either your passport or marriage certificate will back that up.
Pre-nom never changes does it - your Christian/ first name! Hope I’ve got all that right, so I put maiden name or married name depending on which way it’s specified on the form that’s asking. always a good idea to take birth, Marriage and divorce certificates, as a friend of mine had to once, plus passport if you are going to the sous or pre-fecture to do anything official, Mairie also I guess.