Remixing a song and using it would be a copyright infringement. You would be liable to damages and vulnerable to lawsuit. Very likely any legal action would start with a cease and desist order, and could end there if you complied. (This is friendly advice, NOT legal advice, seek a lawyer for that). Just because there is a current game with music that you recognize doesn't mean that it is ok for you to do the same. They may have permission, that song my not be copyright of Square Enix, they may currently be in legal battle, or any other number of scenarios.
Here is a good FAQ for similar question you might have.http://www.gamedev.net/index.php?app=fo ... =rules&f=5
Will using FF music make your game any better. Why not find some free loops or hire a composer for you game and make it unique. I understand the struggle, because I am terrible at music, but it just isn't worth it. My next game is going to have some free music in it, but I hope to be able to hire a composer for some of my games planned for the future.