Itīs very simple:
Cocoon is Pulse on the future.
(SPOILER)
Let us discuss everything that suposedly debunks this theory.

"Fang and Vanille actually prevented Cocoon from falling on Pulse."

First,an holographic ceiling could simulate Cocoon falling.
Second,Fang and Vanille just crystalized touching the ceiling near the image of Cocoon.

Cocoonīs ships were created by the FalīCie and could be time machines.