The archbishop's airship, Soleil, was seen in the Sea of Clouds, but you will need to confront the Vanu Vanu to investigate further.
This quest is available if you have completed the quest The Sins of Antiquity.
Starting the Quest
Talk to Lucia in Ishgard to begin the quest.
Speak with Cid
Go outside and use the Aethernet Shard to go to the Skysteel Manufactory Aethernet Shard. Go northwest to the small stairway and go clockwise around the building. Enter the Skysteel Manufactory and talk to Cid to complete the quest. There will be a cutscene.
Next Main Scenario Quest
After you complete the quest, talk to Alphinaud to accept the next quest: Into the Blue.