FAT systems cannot natively handle file permissions. It just isn't designed to record such information. You have to mount it with a mask that simulates permissions. So in fstab use the "umask=nnn", with the number being the inverse of the permissions you want to have. IOW, if you want permissions of 755, then use "umask=022".
There's also fmask and dmask if you want the numbers to apply to files or directories only, respectively, and you can also use "uid=name" and "gid=group" to set the owner and group name for the drive.
Check out the man page for mount ("man mount") for a more complete listing of options.