There is indeed a process - there are three company’s which do card clearance - visa, mastercard and amex.
I’ve just received a chargeback via a debit mastercard for a booking dot com booking where their ‘host’ refused to refund the money on their offer of a single room without ensuite for a booked double ensuite room.
Don’t take too long though - there are time limits - also you need to show you have a ‘final’ refusal, in my case the refusal e-mail from booking dot com sufficed perfectly. Also mine was a UK mastercard, there is a minimum transaction value of £10, there isn;t a minimum for visa.
The schemes for debit cards are entirely managed by the card companies, it isn’t part of UK consumer protection - maybe there’s more legal backing in France. moneysaving expert as ever has a whole guide for it - for the UK but posasibly the same principles apply across the work as the card providers operate worldwide?
Bon chance!