I have limited experience with Briefcase, but couldn't you:
1: Create a share on both your laptop and desktop PC.
2: Place the file you want synchronized in that share.
3: Create a briefcase on the laptop and the desktop PC.
4: Browse to the file (or use the Run command w/ UNC path to the share name) that is on the desktop PC from the laptop and drag that file into the newly created briefcase on the laptop (and vice versa).
I'm willing to bet you could use your pre-existing briefcases by just dragging the files from the shares you create, making one briefcase handle synchronization for both floppy to the local system and between your laptop and desktop PC. Of course, I could be wrong about all of this (which is why I said I had limited experience
).