J.R.R Tolkien's books, including LOTR, were clearly a big inspiration for both the FF series and the fantasy RPG genre in general. FF games have plots similar to Tolkien's books, basically they have a main hero joined by a group of others to help them on their quests. There is also some influence of Star Wars, although it's subtle. Not really sure about Narnia, I've never read that.
I have to agree with mbuzma on the point of the LOTR. Lot of fantasy games were inspired from the LOTR. And even WOW had some hint of the LOTR in it. As you can guess from the elf. So it seems like for FF there were some of the inpsiration that square enix folks too. Besides square enix has lot of manga and anime authors,so it's easy to get inspiration from.
I think a lot of the influences of the Final Fantasy games came from Tolkien- the English writer,poet, and professor know for being very creative with his fantasy books-that included The Hobbit,and the Lord of the Rings as well. I think he also invented the ranger class that Final Fantasy uses, which includes the Orchs, Goblins,Trolls, and Warqs.