the last two payments I sent by cheque here in France got processed, one by the national electricity provider for about 50€ and the second by an association/company (I'm not sure) for 200€. The last cheque I received, in 2021 (my grandmother reimbursing me the gas refill I did on her car one week before she died), got processed for free by my bank.

But I don't think the chequebook I have can be used to sent money to someone outside of France. And I only have a chequebook because that's how I have to pay my electricity bill.