There are no greek goddesses names starting with an F, because the Greeks would use "ph" for rendering the sound (well, in fact, they had a special letter, which is transliterated as "ph")
Hamadryads - dryad nymphs who preside over different types of trees.
Harmonia - goddess of Harmony and concord. She had a beautiful necklace that brought bad luck to all those who possessed it.
Hecate/Hekate (Trivia) - goddess of magic, witch craft and crossroads. She helped Demeter look for her daughter and then she remained with Persephone as her companion.
Hebe (Juventas) - the goddess of youth, daughter of Zeus and Hera
Herse/Ersa - goddess of the morning dew that nourished plants, a daughter of Zeus and Selene.
Hesperides - nymphs of the evening and of the sunset light, who tended a garden in the west, where the golden apple-trees and other treasures of the gods were kept.
Hestia (Vesta) - the goddess of the hearth and architecture
Horae/Horai - goddesses of the seasons and of the natural portions of time, and, as such, they represent the right moment (in agriculture) and the right order.
Hyades - nymphs who cried so much when there brother Hyas died, that they perished. Zeus transformed them into stars - the Hyades constellation. They are thought to bring rain.
Hybris (Petulantia) - the personification or a spirit of insolence, pride and outrageous behaviour.
Hygieia - the goddess of good health and cleanliness, associated mostly with the prevention of sickness - those ancient Greeks really knew a lot!
And if you want to see pictures of Greek goddesses, just click here or on the button "Pictures of Gods" - in spite of the name of the button, you'll see that there are pages which contain pictures of Greek goddesses, too.