I would translate it as “un homme superficiel”, which pretty much describes the idea of a “face” guy: a man only looking into the physical characteristics of his potential date.

Il est porté sur le physique.

Or

Il attache plus d’importance au physique.

But it does not have the same negative connotation as face guy.

You can say “un homme attaché aux apparences”, which means that the guy gives a lot of importance to the exterior aspects of people, to their appearances.
It has a negative connotation.