There is a limit on how much you can spend per month on a Carte Bleue. If you make a couple of large payments using it, towards the end of the month your card will not work if you have reached the limit. Of course you can have greater limits but you would be silly to do so. Not many people have credit cards.
There is also a limit on how much you can spend in cash. So cheques are required.
Elderly prefer cheques. And why not. It helps them budgeting.
If you think about it, it reduces fraud and all the associated costs with that. So it may be (sit down for this) a better and more a cost effective system.
I am interested to know why you ask such a question.