Ah, long time since I was in the UK, Our "push" thing may be similar to what you call a standing order. I do know that far more French still use cheques than is the case in the UK, you would think that because of that the suppliers would have better method to deal with them. Then again, as their aim is to get as many as possible to let them take the money straight out of the bank account, they would hardly make other methods easy. Bouncing a cheque ( known as a "cheque en bois" wooden cheque ) is not an offence here, but it can get the writer banned from banking.
Post dated cheques are a huge thing here, the french health service is a "re-imbousement" type.You visit a doctor, or hospital , pharmacy etc, you pay them and then you get a percentage of that money paid back into your bank account by the health service within a few days to a few weeks ( private insurance, if you have it "tops up" any difference ). Because of this delay, many people will "post date" cheques for medical or dental work, or expensive medicines. The doctor, dentist etc agree to present the cheque to their bank, only after the patient tells them that they have received the money from the health service.it would be far simpler , cheaper, and less paper shuffling and IT admin, if the system was free at the point of use, and the system then paid the doctors etc.
The doctors , medical practitioners , dentists, pharmacies, hospitals etc do not want that.