Europe used to have two significant card networks of its own: Maestro (owned by Mastercard) and Visa Europe (previously owned by various European banks). But Maestro is dead now and, a few years ago, Visa Europe merged into Visa.
There were a bunch of national networks but they're slowly dying I think. The UK's Switch debit card network got rebranded as Maestro and then killed, for example. The UK still has something called Link however (used for ATM withdrawals and I think nothing else).
Fewer and fewer banks supports it. It's obvious when looking at the neobanks' offers: https://www.zupimages.net/up/24/07/zbua.png ("Réseau CB: Oui [yes] / Non [no]"). A shame as the whole French payment network now relies almost solely on Visa, a $500T US giant.
the italian "pagobancomat" system[0] (pay from your CC with an ATM card) is still alive and well, all ATMs and POS support it together with visa/mastercard. There's also an online payment system but I've not seen it used.
Most plastic you get these days supports both that and visa/maestro.
There used to be Eurocard, but it merged with MasterCard a couple of decades ago. Most countries had domestic debit card networks. Some still have, while others replaced theirs with Visa / MasterCard debit cards.
SEPA is basically free and instant. There are some shortcomings but even with them there is hardly demand for for any other service (why would consumers decide to use anything but banks transfer and/or credit/debit cards when the fees are so low?)
There were a bunch of national networks but they're slowly dying I think. The UK's Switch debit card network got rebranded as Maestro and then killed, for example. The UK still has something called Link however (used for ATM withdrawals and I think nothing else).