It took me a while to find this as well when I first needed it. Unfortunately, when SE added it, they failed to inform players of where the option was -_-;
To find the file repair scan, open up PlayOnline, but don't log in. On the screen should be the page you start at with your account login and a bunch of options along the left side. The fifth option down should be "Check Files". Once in the Check Files section, select what program you want scanned (POL, FFXI, or TetraMaster). It will then scan through all your files (takes around 20min give or take depending on PC speed, etc). Once done scanning, it will inform you of any corrupted files, list them out, and offer to fix them for you. If you tell it to fix the corrupted files, it will then connect to POL to scan all of your files again and then download and install the files that were corrupted. The process as a whole takes a while, but its well worth it to not have to reinstall FFXI from the start.
Hope this helps and that you can get your game working again.