Sazh has been dubbed both "Chocobro" and "Chocofro" by his adoring legion. And thanks to Gadot's expy mention he is now called (by the fans that hate him) "not-Wakka".
Snow was nicknamed "Mr. 33cm" as mentioned above due to his rather large... feet.
And at 6'5/6'7 (accounts vary), his "feet" are actually small for his size.
Galenth Dysley / Barthandelus has recently been dubbed Superpope/SUPAHPOPE!, mainly due to his fondness for transforming into a mechanical monstrosity and beating the party to a bloody pulp. His own Menvra is also called Hedwig. He's also been dubbed "Barty" by some.
Snow's Gestalt mode has been dubbed "The Motordyke" by a portion of the fandom.
Orphan, the final boss of the game, was referred to as Oprah rather frequently during early squabbles over its name.
Aster Protoflorian has been given the name Bulbasaur.
Doesn't Cocoon look an awful lot like Meteor? It sure does in the ending. Vanille and Fang even use The Lifestream from stopping its descent.
Sanctum soldiers and citizens use something called "manadrives" to cast magic without the threat of becoming l'Cie. They serve the same function as Odine Brand para-magic machines, just with a different name.
The entire battle system is apparently based around Chainspell, although it is expanded to all attacks rather than being a Limit Break. Someone more familiar with XI could confirm/deny this more readily.
The concept of l'Cie, magic-using humans who mutate into demonic monsters and whose souls solidify into a physical, crystalline form and are forced to fight a war as avatars of Physical Gods are based on Espers, who are...magic-using, mutated humans whose souls solidify into a physical, crystalline form who were forced to fight a war as avatars of Physical Gods.
The game starts with the ex-Soldier and the black guy on a train. They then proceed to fight a giant scorpion robot.
The entire dynamic between Fang and Vanille is mined from a single boss battle from Final Fantasy III: You fight a boss named Hecatoncheir in order to collect the Fang of Earth, four of which unlock the path to the Crystal Spire and the end of the game.
Gilgamesh was intended to appear as a regular character; a fal'Cie with giant swords. Fridge Logic dictates that he was likely supposed to be the ultimate opponent of Titan's Trials as opposed to Attacus, as Attacus uses the exact same progressive battle tactics that Gilgamesh did in Final Fantasy XII, and you are arbitrarily given the store Gilgamesh Inc. as a quest reward for finishing half of the Trials fights. Getting this store as a reward for beating their namesake would have made more sense.
What Could Have Been: According to the Final Fantasy XIII Ultimania Omega, the development team at one point considered making Vanille the official main character of the game, but dismissed the idea as they had already released a trailer and art featuring Lightning in that role.
The fal'Cie Siren wasn't just in the Pompa Sancta, but is Bodhum's fal'Cie. However, since the player never gets visit Bodhum properly, the only time one can see Siren is in cutscenes.