That's definitely not the case. Many people would have credit cards, but there's a lot less incentive to actually use them than there is in the US, because the interchange (paid ultimately by the merchant) is capped at 0.3% in the EU (whereas in the US it can be upward of 3% on high-end cards). The interchange pays for the 'reward' schemes that US card issuers provide, largely. Without those, why bother?
I've a credit card, but I essentially never use it, except when visiting the US (where some vendors actually refuse debit cards, or at least used to).