Earlier quoted context omitted.
Credit cards are much less heavily relied on in Europe than in the USA. Europe basically runs on debit cards that every kid can have and where the fees are minuscule. There are countless banks providing the service and everything is highly regulated. On top of that, Europe still curbed Visa and Mastercard several times for antitrust behaviour. And the idea that physical money primarily aids social fraud, money launde…
I'm not sure which European country you're talking about, but in France most transaction are now done by card. Yes it's mostly debit cards, but they're still handled almost exclusively by Visa and Mastercard. Many banks have tried to start other electronic payments independent from those 2 (for example Wero) but it doesn't really get any traction. So I don't see how the duopoly is any less powerful here.
Some card fees are capped by the EU: https://www.visa.co.uk/about-visa/visa-in-europe/fees-and-in..., quoting "From 9 December 2015, European regulation on interchange fees (Regulation (EU) 2015/751 of the European Parliament and of the European Council of 29 April 2015 on interchange fees for card-based transactions, “the IFR”) imposes interchange fee caps on most product types within the European Economic Area (EEA).".
It is true though that French banks have huge fees even for debit (0.20%) compared to, for example The Netherlands (0.02 eur).
So the doupoly is not as powerful everywhere, but I have no clue why the difference.