In the US charging a minimum for card transactions is usually a violation of your contract with Visa/Mastercard, and possibly a violation of the law in 10 states [1]. Are there similar contracts or laws in France?
That's about checkout fees, not minimum charge amounts. Minimum charge amounts used to be forbidden by basically every merchant agreement, but thanks to Dodd-Frank and a lot of retailer lobbying, such contact terms are now illegal. Card issuers must allow a restriction on charge amounts (no more than $10 IIRC) if the retailer so desires.
Here in Sweden you're not allowed to charge any sort of additional surcharge, but you are allowed to simply refuse accepting payment with Visa/Mastercard for purchases under a certain amount.