Ok, pop out of  the tower and into the Falcon. Go to the castle of Giott. Go to the King's Chambers. He will give you Luca's necklace. Then go see Cid. He's in the dwarf infirmary.  And he's off to upgrade the Falcon. And just like that, he falls asleep (but not before he fixes it.) Ta-da! Get in the airship and your ready for side quest!!