Thought they use Sepa
Sepa is how my kid's daycare debits me each month, or how I transfer money to other accounts (most bills are direct-debit, but sometimes I get a one-off invoice and I have to transfer the money myself).
But for the small person-to-person type thing, paypal is the defacto here (sadly).
SEPA uses your IBAN (account number), and one can also enter this account number for payment, implicitly allowing the store to withdraw money from it...
I wish. The small inconvenience of putting in an IBAN and a matching name instead of just an email address is already enough for many people to default to paypal. Just happened to me again yesterday, the guy preferred to bring cash next time we see each other instead of just receiving my info via text.