It's quite simple. FFXI doesnt play from the disc. It only needs the disc for starting up. The actual game is installed on the HDD. So you're going to need to reinstall the game from the disc. Remove everything, put in the very first disc, and find yourself something to do for the next... 20 hours.
Wish i could be more specific, but i havent played FFXI on the 360 ever since one of the updates couldnt download anymore because the game took up more space than my entire 360 HDD could handle. Which is to say, years ago.