Hmm, that part about the Pulse fal'Cie searching for the portal makes indeed no sense.

Though I'm sure the fal'Cie didn't create Cocoon for soul harvesting because they simply didn't exist before it was created. They were purely made to maintain Cocoon and their creator was a goddes who crafted them after the image of the Pulse fal'Cie who in turn were made by the Maker.

Then again, perhaps Barthandelus is able to create new things for Cocoon? His focus is to be its architect after all. Though I'm sure Lindzei lay the foundation for his work.

They say the fal'Cie made the Arks in preparation for battle against the menace that lurks beyond. Where is this "beyond" of which they speak? Do they mean Cocoon, and the demons that dwells within? If so, they are mistaken. The legends of the Arks date far before that sphere was even crafted; whispers even hint at Arks displaced around the time of Cocoon's creation, spirited away to be hidden in its shell.
What, then, is the "menace"? What distant threat confronts us, and to what purpose? The gods vanished from this place. Are they now residents of the "beyond"?

Cocoon was built in order to counter a threat from "beyond".

Sorry for the quoting all the time.