|You misunderstand what a file system is.|
Floppies can only be formatted to FAT12. They are far to small to warrant any other file system, not even FAT16 or FAT32.
The fact that Windows XP is installed on an NTFS files is irrelevant, Windows XP can still read FAT and all its variations regardless of which file system it is installed on. The same goes for Windows XP installed on a FAT32 files system, it can still read NTFS partitions.
You problem is that the floppy disk is corrupted. When formatting a floppy the formatting procedure can isolate bad track and ignore them with a reduced capacity. But it cannot do that with track 0. Track 0 is absolutely required in order to store the Boot Record. The only thing you can do with this floppy is bin it.