.. If I were to grant him a county and make him my vassal, will the kingdom of France fall into the Byzantine Empire when he inherits?
no
Instead he'd leave the empire together with the county.
You have to grant him an equivalent-tier title to the one he inherits. That way, when he inherits, the title you granted remains his primary title and he becomes your vassal. Otherwise, if he only had a count title within your realm, upon inheritance, the independent King of France title would become his primary and he'd go independent. This occurs even with the "Controlled Realm Inheritance Law" enacted.
Note that this is different from claim wars, where you can give them any landed title, including a barony, and they'll remain a vassal even after you press their claim.
In either case, be careful with the title you give him though. I was just in the middle of a claim war and had the claimant lose his land due to a internal de jure holding war. He then ended up in another court and I couldn't bring him back, so he become independent when I won the war. I probably could've requested them to end the war or handed out another title, but didn't pay enough attention to what was going on because I was busy fighting an external war...