Can't say, but they should work just like a cassette player should work (dunno if they've take those up either). They rely on tension keeping the media to the head, so micro-g shouldn't have any real impact on it.
I think the floppies themselves would be fine, inside the spacecraft.
Outside the spacecraft could be a problem for the drive, but the floppy likely still ok.
If there were any electrolytic caps on the PCB (unless they were space rated parts with special seals) they would likely spew their guts. Still if many were Tant types they might be ok. Mil spec rated axial Tants with glass end seals are ok in a vacuum. For some space rated parts the whole assembly is sealed in resin to help protect it. Most electronic parts, resistors, ceramic caps, IC's and transistors are ok in a vacuum, but not always. This is one thing that makes "space rated" parts more expensive and Ideally the IC's are also radiation hardened too. Also likely many lubricating oils would start to evaporate quickly.
So it could be a plausible scenario in a Sci-fi movie to have a floppy working in space, say where an astronaut put one as a "software upgrade" into a slot on the side of a satellite or something. This would be much more plausible than all the sound effects of engines running and guns blazing in space when there is no sound there, but this classic "sound in space" error has been made in nearly all Sci-fi movies, except perhaps 2001 Space Odyssey which is the only movie I can think of , off hand, that got this correct. You could hear sounds inside the spacecraft (as its gas filled) but outside no sound so they just played nice classical music.
Also, the decompressing spacecraft is a good model to explain to Physics students that nobody has ever been sucked out of a plane, they are pushed out by the air leaving. If the astronaut with his helmet on could hold on inside long enough for the air to leave the craft to space, the forces pushing him out the hole in his craft would disappear.