Cids aren't the only repeating thing. there are a few other inter game similarities.

Biggs and Wedge are in many later versions. certain weapons are found in numerous games. But one of my personal favorites is the word Crescent.

FF1: Crescent Lake
FF2: Crescent (weapon)
FF5: Crescent Town
FF8: Crescent Wish
FF9: Freya Crescent

Also in one FF there was an enemy named Crescent. Not in all but definitely not a coincidental trend.