American Express has really targeted the French market, there are all sorts of small stores (like bakeries, pharmacies (not American pharmacies - only medicine and very closely related stuff like creams and diapers) and similar size) with proud "Amex accepted here" signs. There was even an Amex program a few years back giving 5euros back on transactions of more than 20 euros in small shops like that.
Ironically this may have been true at one time but Amex is now one of the best card providers to deal with as a merchant as they have a very clear and transparent dispute and then appeals process. Visa/Chase seem to be impossible to win.
This wouldn't surprise me, given that Amex does have a consumer reputation for being very friendly for disputes. That factors in two ways: a successful dispute means that the merchant is completely out that money, and every dispute also costs something like $25 to handle regardless of whether the merchant ultimately wins or loses.
It's much easier just to model this as an additional merchant "fee." If a card tends to dump fraud liability onto the merchant (and here we're talking about fraud that the merchant really isn't in a position to prevent, but the card issuer/network might be) then this simply increases the cost born by the merchant who accepts the card. Of course it's extremely difficult to estimate these costs, which is probably a desirable feature for card issuers/networks, since lack of price transparency is usually helpful if one wishes to overcharge for things.
Used to be every year, Amex in Canada would run a "Shop Local" promo where you'd get $5 back on a transaction over $10 at smaller places x5 in a month, and let you look up who's a part of the program on a map.
Then you'd visit a lot of them and they'd claim to not accept Amex!
