Wero is not French, but it has replaced France's Paylib. It's pretty awesome and seems to quickly have replaced all other apps (Lydia, PayPal) for small payments in my friend and family circles. I'm excited to see it expand to PoS payments.
No single country can claim ownership because it's an EU initiative. iDeal was one of the first and relatively easy systems across the EU, but it's hardly the predecessor.
Wero also does peer-to-peer transfers which iDeal doesn't (unless you use iDeal to pay for tikkies but that's still two apps). The new system is not just an iDeal rebranding.
Directly, without Tikkie? That's really interesting. I wasn't aware of that yet. My impression was indeed mostly a rebranding and expansion of iDeal.
The greatest force of Wero is that, being from a bank consortium and not "another app", you can send money to people that don't even know the system exists as long as you have their phone number because the money will go straight to the bank account registered with this phone number.
You don't need to register to the service to receive money so basically anyone holding an account in a compatible bank can receive funds instantly. Which means, as the person sending the money, you don't have to tell your friends to install it.