There is indeed a Tower of Babil [sic] in FFIV.
The Tower of Babel was originally the creation of the Babylonians in the book of Genesis. The people of Babylon, who at the time all spoke a single language, built a colossal tower in an attempt to reach into the Heavens. Ultimately, since the tower was built for the glorification of mankind* rather than in honour of God, He struck it down (this part of the story doesn't appear in Genesis, but does occur in some early Jewish texts) and confused the language of the people. This is suggested as being the cause of the huge variety of languages spoken on Earth.
* "Then they said, 'Come, let us build ourselves a city, and a tower with its top in the heavens, and let us make a name for ourselves; otherwise we shall be scattered abroad upon the face of the whole earth.'" (Genesis 11:4)