I think France is a bit of an exception because there's the CB network[1]. Most cards here are either CB/Mastercard or CB/Visa and a lot of stuff uses CB by default if I understand it correctly. According to their website the network accounts for 65% percent of national transactions[2] but I'm not sure of how to interpret their wording.

[1] https://en.wikipedia.org/wiki/CB_Bank_Card_Group

[2] https://www.cartes-bancaires.com/cb/chiffres/