I seriously doubt it's worth it.
First question: Does the G3 have Firewire? My memory is fuzzy, but most of those old G3s didn't even have USB. They just had the the old Apple Desktop Buss and SCSI. Without a firewire port, you've got no way to get video in or out of the computer.
IF you do have firewire, you probably need to update the OS to 10.3 or 10.4 (Check the Apple website to see if a G3 even runs with OS X) Next, you''ll probably need to add a lot of RAM and probably a bigger hard disk. We think of hard disks in hundreds of GB, but back in the G3 days 400 MB was considered a pretty good size, especially in a school.
If, after spending all that money, you can get Final Cut to run at all, it would probably be so unbelievably slooooooow as to be useless. As a guess, a render that takes 10 seconds on your G5 might take something like 15 minutes on a G3. (That's 2 orders of magnitude slower. It might be worse than that.)