If it were a Dyson Sphere it'd be getting power from the star in the center of it. It's not. The star is just Phoenix, another Fal'Cie. Cocoon gets most of its power from Orphan. Also there's no way people could live on the inside of it as they'd be burned up.
It's more like the world of Pryan from The Death Gate Cycle. A hollow sphere with an artificial sun in the center that people live on the inside surface of.
Coming 2014 calling it I'll be reverend on the internet by my predictions. Haters can doubt all they want but they can't deny that Versus' arrival is imminent.