You need to mount floppies before Debian can read them. (See "man mount".) For mounting floppies you need to have a line for /dev/fd0 in your /etc/fstab and to mount floppies as a normal user you need to belong to the "floppy" group. You also need to unmount the mounted floppy before taking it off, so you won't lose any data.
Or you can install mtools, which can read vfat formatted floppies without mounting. (After installation check out "man mtools".) You can also format floppies with mtools easily: just type
from the command line. Also, there's a special file manager for mtools, called MToolsFM and you can install both mtools and MToolsFM with a single command:
apt-get install mtoolsfm
Hope this helps.