Although it's probably unlikely to happen, one FF character I would really like to see a world event based around is Terra Branford from FF6.
Here's my idea of how the story may work and a list of three FATEs that would fit:
1. In the house, in a heartbeat
Location: East Shroud
Requires Level: 16
A mysterious green-haired woman in red robes has been found unconscious in the forest. Protect her from the Ixali and find out if she is friend or foe.
After completing this event Terra will awaken and speak to you about how she comes from another universe, but her connection to the Espers has somehow caused her to awaken in this unfamiliar world with little memory of her past and she needs help getting back.
2. Twelve save the children
Location: Southern Thalanan
Minimum level: 28
In this FATE a group of Amajaa have imprisoned children to be raised as thralls of Ifrit. Terra has a soft spot for children and simply cannot abide such treachery, so you join forces with her to defeat the beastmen and unlock the cages.
In the quests following this fate you learn that the Player Character has a lot in common with this stranger - both have powers they need to control, and both are fighting an empire that makes heavy use of "magitek" machines.
3. Welcome to the machine
Location: Mor Dhona
Minimum level: 50
This is a three-phase event. The first phase is an escort through Mor Dhona where you must protect Terra from the Garleans and their Magitek. In the second you fight alongside her against magtiek enemies of the Gestahl design from FF6 who have suddenly appeared. In the final phase you fight a Gehstahl Colossus boss (~800k HP) and Terra transforms into her Esper Form and gains new abilities.
After the fight is over, Terra will thank you for helping her gain insight into her true nature and powers, and will be allowed to return to her true timeline.
Terra's battle quotes:
"Get away!"
"I must be strong..."