But the underlying payments network isn't necessarily Visa/Mastercard's. In the case of France, there's Cartes Bancaires https://www.cartes-bancaires.com/ https

But the underlying payments network isn't necessarily Visa/Mastercard's. In the case of France, there's Cartes Bancaires https://www.cartes-bancaires.com/ https://www.cartes-bancaires.com/, which you can pay through regardless of your card type (Visa, Mastercard, Amex) as an alternative over paying through the Visa/Mastercard/Amex networks. And of course with GDPR, there are actual restrictions on how Visa/Mastercard can monetise your transaction history, and with banking regulations, how much of a cut they can take.