Aside from looking cute, minions don't do anything at the moment. Here're some suggestions on making minions more relevant to the game.

Town Abilities
Summoning a minion grants the player benefits in town. The abilities need not be unique to each minion. Instead, have a few categories of abilities and have a variety of minions within that category.

Examples of abilities:
Pick-up
If a player wanders around town with a minion with this ability, there is chance the minion would pick up an item. Items could include gil, vanity items and maybe even materia.

Rush Hour
Extends the duration of a player's sprint.

Catalogue
Shows player all items sold by NPCs in the town. Players would still have to approach the NPC to buy the item.