Your business place, assuming a public business, is indeed that: a place open to the public by default.
In France (and, as far as I'm aware, most European countries), there is a very clear line: either your business place welcomes the general public, or it does not.
Once you fall in the first category - and, as soon as you're selling something in that business place, you are in that category - then you must have very strong arguments if you refuse to let a prospective customer in or even if you refuse to sell to a particular person the products or services that it is the purpose of your business to sell.
Those arguments usually boil down to either (i) some law preventing you to sell something to that prospective customer or (ii) that prospective customer actively disturbing the public order or presenting a high risk thereof (eg: they're a thief, they're drunk, they can't prove that they will be able to pay, ...). Of course there are provisions for specific settings, but which merely soften the (ii) to allow filtering on public safety grounds for places welcoming more than X simultaneous guests - including eg nightclubs and such.
Anything not in falling into these exceptions is just what it is: discrimination. And actually, this seems very sound to me. The fact you own a business puts you in the public world: you may not refuse to serve someone because you don't like them.