We use still some floppies and it is important that we back up them, because it is a long process to create the disk and if it fails, the time to redo the disk is longer than restoring a backup or the know how is not there.
To backup a floppy disk or any other disk we use the dd tool, including hard disks, in new versions of Linux it supports files larger than 2 Gigas.
$ dd if=/dev/fd0 of=/backup/floppy_backup.dd
To restore the backup into a fresh floppy (note, you will loose any other information in the floppy):
$ dd if=/backup/floppy_backup.dd of=/dev/fd0