The story I heard was that the forage cap was originally a shako, War of 1812 style hat, tall crown with a bill. The crown was supported by a pasteboard or starched cloth insert, which wilted with exposure to moisture. Also could collapse if somebody sat on it.

Also heard that the soldiers thought the insert looked "foolish" and just took it out.
As for the kepi, it's just a little old hat. I don't know the story behind it.
Zou wears a fez, which doesn't keep the sun off any better than a kepi. Would much rather wear a Hardee hat or a slouch hat!
Zou