You are thinking about the "droit au compte" (right to a bank account) https://fr.wikipedia.org/wiki/Droit_au_compte but I think there may be some confusion. People exercise their "droit au compte" by making a request the Banque de France, but they do not have an account there: Banque de France designates some regular commercial bank which is then legally obliged to provide them with an account. The French Wikipedia page says that, in practice, this is usually La Banque postale: it's a pretty normal bank that I don't think anyone discriminates against.

In the UK the biggest banks have to offer a free basic current account.

Requirements basically boil down to acceptable ID

And you think those landlords would rent to cash payers?

In France, you can't buy a car with cash. Not exactly a shining example.

Banks have been around for hundreds of years. All I'm proposing is that there is a legal right for people to hold a bank account of some form, where they are able to put their money so they don't have all their life savings in cash under the bed. I'm not suggesting that we ban cash at all, just that people have a right to securely store their money and the option to use cashless transactions if they choose.

Being legally required to hold a bank account use cashless transactions is just as much of a violation of one's rights as being barred from opening a bank account and being forced to use cash for all transactions. Two sides of the same coin, so to speak. It's not about allowing people to transact in cash, but allowing them alternative choices, all of which should be legal.

If you can't hold a bank account (because the banks have decided you're not allowed one for whatever reason), you need to use cash for everything. This means you always have a relatively large amount of cash on you. Not only are you now at greater risk of burglary or robbery, the consequences of being a victim are now even greater. You also can't put money in a savings account, or pay for things online.

I've had my house burgled and had large amounts of cash stolen from me before. There was nothing the police could do. Even if they caught the burglar, the money wasn't coming back to me. It was a significant hit to my personal finances at the time.

Bank accounts and cashless transactions aren't just a way for the government to keep tabs on the population, they're also a form of security for the general population.

"Not everyone has those" seems probably a USA-related perspective as people not having ID is a problem there; but in many places in Europe it's normal to assume that everyone does have a valid ID; you're required to get one when you become an adult, you're required to report if it gets lost/stolen so that it gets blocked and replaced. You don't have to have that ID with you, but not having a passport or ID card at all is a misdemeanor. Even homeless drug addicts generally have them because it's necessary for various things e.g. social services.

If someone needs banking services (or, really, any services from anyone) but don't have a proper gov't ID document then would be considered normal to require that the very first thing they'd need to do is to get/replace that ID. And if you have that, then that's all you need for basic banking services.

I'm not proposing that bank accounts are a legal requirement, but rather that access to banking is a legal right.

Yes, because when the management of the money supply is put into private hands, that has worked so well. Company scrips [1] were great for the people.

You haven't actually proposed a solution. Who should control the supply of money? Private companies? Because they have an even worse track record to governments.

[1] https://en.wikipedia.org/wiki/Company_scrip