EMV2-compatible debit/credit cards work pretty widely. The real issue is that some countries have locally-popular cards that don't work in that scheme (Dutch old Maestro variant, some german cards, etc.) or have very annoying compatibility issues (my old "Visa Electron", once very popular in Poland and which tripped UK card systems like crazy) and availability of card payments differs across EU - capping card fees and speeding up transactions thanks to EMV helped there a lot, but I remember hearing stories of Italian shops in touristy areas getting card readers... because of Polish visitors, who were accustomed to wide availability of cards (last local bastion of cash only was farmer's market nearby - now every more established stand has one)