Miam!

(la) faim = hunger (pronounced like "fin")

avoir faim = to be hungry
mourir de faim = to be starving
rester sur sa faim = to be disappointed by something, that didn't live up to expectations
laisser (quelqu'un) sur sa faim = to disappoint (someone)

E.g.: je meurs de faim = I'm starving
ce spectacle m'a laissé sur ma faim = I was expecting more from this show