That sounds like one of the oddities in retro-computing that could be enormously fun to investigate in detail, if reproducible.
Unfortunately, I don't have or ever had a Franklin, and acquiring one just for that would be a bit much (with no other interest in the machine besides that, it would also be a waste).
I once bought an Apple II just to resurrect one old floppy disk. Many things went wrong, and I actually ended up buying two of them, and a bunch of other stuff, before it was all over. The story is here:
Makes me wonder if the individual bits on an old floppy could be picked up by magnetic film. If that had sufficient resolution, you could then just photograph the film, and do some image processing to read the bits. There's a bit of work to then decode the actual data.
Not quite "picked up by magnetic film", but nowadays it's very common do use things like KryoFlux, which essentially reads the magnetic flux changes on a very low level, and therefore provides a very detailed (for almost all intents and purposes: 100% faithful) image of the actual disk. Not just its filesystem or any other higher level.
Reading in a disk drive is also usually entirely nondestructive (barring any mechanical issues), so that's a very good solution already.
Unfortunately, I don't have or ever had a Franklin, and acquiring one just for that would be a bit much (with no other interest in the machine besides that, it would also be a waste).