Agree with Fu Ma

French men get reputation of being very romantic. They know how to flirt with girls, show passions in public and sweet-mouthed. Don't know much about how things goes between you and him. But if you didn't get confirmed from him that you are his girlfriend, you might just misunderstand his intention from his words and behaviors. Even you kissed or maybe already had sex, he might only treat you as a normal female friend. For him, that's his casual life style, not a big deal, but for the conservative girls like you, you might take all those as symbols of a gf.

How to confirm, you may ask. Well, did he ever introduce you as gf when you hang out with friends or when you run into his friends on the street?

Don't take it too serious that he didn't invite you to his family dinner. It's too soon for meeting parents. But do ask him if he treats you as gf and you are exclusive dating-- if you are so frustrated about which stage your relationship is.

Good Luck