Well, to be technical a Faune is from Roman Mythology. If it were Prélude à l'après-midi d'un satyr...
You're right, of course.

But then, to be technical, the poem does start "Ces
nymphes, je les veux perpétuer" (my italics). (Then again, the Romans did adapt nymphs too.) Perhaps I'm being influenced by Szymanowski's Myths, but I wonder if Mallarmé didn't have Pan in mind.