You will not encounter Famfrit until near the end of the game. However, you will not meet Famfrit alone. He is actually summoned by Dr. Cid. After he loses about half of his heath, Dr. Cid summons him to his aid. Focus all your attacks on the Esper, because he is invulnerable with him out. He is a Water type; use Oil on him and shoot some Firagas at him. You can also use your summoning abilities to summon Belias. If he survives long enough to use his final attack, the Oil will double the damage. He already takes double damage from fire attacks, so it will do quadruple damage. When he has been defeated, you can then focus on Cid.