I have played several of the Final Fantasy games and know that many of them have manga counterparts.
Having finished the games, I wouldn't overly want to read a retelling of the story I spent hours grinding through. However, If they are spin off stories I would be interested in reading them as I enjoy the interesting characters and fantasy world.
Do the manga series retell the games' stories or do they have alternate content in them?
There are indeed allot of manga/novel/manwha adaptions of Final fantasy games,anime and movies and there are indeed some with alternate content to the already known storys or even totaly new storys. As found on final fantasy released media wiki
Many Final Fantasy games have been adapted as novels and manga series. With the advent of the Internet, web novels and digital publishing have also become common. These stories act as companion pieces, offering an interpretation of the game's events or expanding the plot of the games by depicting additional scenarios.
Final Fantasy II Mumu no Meikyu, Is the Novelization of Final Fantasy II written by Kenji Terada
Yūkyū no Kaze Densetsu Final Fantasy III, Manga adaptation of Final Fantasy III by Yū Kinutani (art) and Kenji Terada (story)
Final Fantasy: The Spirits Within, Novelization of Final Fantasy: The Spirits Within by John Vornhol
Final Fantasy Crystal Chronicles ~Hatenaki Sora no Mukō ni~, Manga adaptation of Final Fantasy Crystal Chronicles by Ryunosuke Ichikawa (three volumes)
Final Fantasy IV, Two-volume novelization of Final Fantasy IV
Final Fantasy IV: The After, Novelization of Final Fantasy IV: The After Years
Adventure Log, Official Final Fantasy XI webcomic
Final Fantasy XII, Manga adaptation of Final Fantasy XII by Gin Amou
Final Fantasy Crystal Chronicles Ring of Fates 4 Komaansoroji Komikku, Manga adaptation of Final Fantasy Crystal Chronicles: Ring of Fates (2 volumes)
Final Fantasy XIII Episode Zero: Promise, Series of web novels written by Jun Eishima and first published on the official Japanese Final Fantasy XIII website, depicting the thirteen days leading up to the events of the game
Sō no Kizuna, A side story to Final Fantasy: Unlimited
Final Fantasy: Unlimited After, A series of web novels published on the official Japanese Final Fantasy: Unlimited website, which continue the story of the anime
On the Way to a Smile, Collection of two novellas, "Case of Denzel" and "Case of Tifa", set in Final Fantasy VII's continuity, written by Kazushige Nojima and published in the book Final Fantasy VII: Advent Children Prologue
Final Fantasy XI ~The Out of Orders~, Manhwa set in the Final Fantasy XI continuity, by Kim Byung Jin (art) and Kim Sungjae (story)
Final Fantasy XI, Series of novels set in the Final Fantasy XI continuity, written by Miyabi Hasegawa
