When fluorine melts and boils it stays a diatomic molecule, that means that the bonds between the flourine atoms do not break. A high melting point indicates that the molecules fit to gather tightly for geometric reasons, and more energy is therefore it requires to break apart the intermolecular forces. As far as boiling goes the molecular mass and the intermolecular forces are important. As molecular mass goes up the energy required to create boiling goes up so the boiling point goes up. As molecular mass goes up size goes up and London force goes up. Since F2 has no other intermolecular force than London, and since it has a relatively low molecular mass, it's BP is relatively small.
Because of its three-dimensional polymeric structure, AlF3 has a high melting point.