7.6? Ouch, that's 12+ years old! Are you sure you have content worthy of the effort/potential expense of transferring it?
http://www.versiontracker.com/dyn/moreinfo/macos/4192 is an FTP that works on older Mac OS's but I don't know beyond that. FTP may be your best option. There's no such thing as SMB for OS 8 and below, so a direct ethernet connection is out.
P.s.: Its a Mac Quadra 9500, which had some card inside for the old imagesetter (varityper). The system is 7.6 and a panther software rip. So I can't put files of 300 MB to a diskette. We tried to buy new mac but they not have the right slot for the "card". And upgrading the software RIP for the new mac it just cost too much.