I looked at it and got the impression that it was BNP's low cost product, aimed at a younger audience, perhaps with no banking record.

I use Boursorama Bank in France and they're pretty good. Setting up the a/c and transferring over from HSBC FR was relatively painless, though they dropped a few of the direct debit mandates that I had to recreate manually. I think the account is free as long as you actually use it actively.

Orange Bank is another option in France which is free for basic current account activities, although they don't offer Livret etc.

The best way to do this in France seems to be to keep a "legacy" bank just for handling savings without a current account (that way you don't pay for current account, card etc.), and use one of the free challenger banks for current account, direct debits etc.