Grandes Ecoles -> French Degrees - recognized by the state vs issued by the school

I have an offer for MSc in Business issued by a Grande Ecole. It isn't "recognized by the state" in France but is simply issued by the school under it's own authority.

The school is fully accredited locally (and quite a famous and good one), and carries international accreditation (AACSB, EQUIS, AMBA).

How big a deal is the not "recognized by the state"? I know it caused problems for one contact who couldn't use the degree in Chile because all their mutual recognition is based on Govt to Govt qualification equivalence.

How about North America? Europe?