Earlier quoted context omitted.
A mastercard debit card works much like a credit card. In germany for example, your standard "debit card" is your banks card and in online transactions, you just enter bank account and the banks identifier. It's a legacy way of paying that dates back to the eurocheques. It's comparable to the Card Bleue in France which is a system that exists pretty much in France only. This fragments the market.
The Carte Bleue system is more or less deprecated/integrated now, AFAIK they can all be treated as Visa cards
French people regularly use the term "carte bleue" to mean "debit card" (and most of the debit cards still feature the legacy "carte bleue" logo). Even worse, most of them say "carte de crédit" (credit card) when they really mean "debit card", because credit cards are very uncommon and people don't know the difference. I have no statistics, but from my personal experience, credit cards not linked to a bank account barely exist here.
On the other hand, we have a lot of companies offering short-term, small-amount credits easily — directly on your bank account, without a dedicated credit card. Maybe those play the same role as credit cards in the US?