Hmmm...Well I've just pulled the cable off of my internal floppy drive and got DF0:

? on the screen. So it looks like you could have a faulty cable, a wrongly connected cable or a faulty floppy drive. It is easy to connect the cable wrongly by having it too far to the left or right and missing some pins. Likewise, you can have the cable too low and miss a whole row of pins.
In normal use jumper J352 is set to INT and jumper J351 has no jumper on it. An external floppy drive connected to the position labelled FLOPPY at the rear of the A4000 works fine, even if I do not have the lead connected to my internal floppy drive. The external drive on the position FLOPPY is DF2 by the way.
DF1 is a second internal drive connected to the same lead as DF0: and you adjust the jumpers accordingly. You put a jumper on J351 if your second internal floppy drive is 880K, but leave the jumper off if it is 1.76MB
Yeah I'm also looking at the A4000 User's Guide for that last bit :-D