You are correct. But they are several reasons why the situation might seem complex for a foreigner.
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?