So I got this info from the admissions team. Is this fine?
GMBA is certified by the CNCP (Commission Nationale de la Certification Professionnelle) under the RNCP registration code 35787
It seems ok to me, although I'm no expert. I looked at the offical RNCP register (official registar for various certifications and diplomas) - I can't post links here but if you google "RNCP 35787" you'll find it.
It seems that what you mentionned is the EDHEC MBA, and it looks like it's officially recognised as a masters grade at it's RNCP level 7 (RNCP level 6 is a bachelor for example, and level 7 is a master or MBA or EMBA). So, I'd say it should be recognised as a masters level everywhere in France.
The weird thing is that the code provided to you by the school is the MBA and not a MSc, but you mentioned it's a MSC in your initial message.