There is a two-stage fix offered by Apple which saved me in restoring my new iMac 27 5K from my old FW800, 1TB G-Drive. This fix worked for me, as I could not figure out any other options except trying to mount my old iMac mid-2010 internal HDD on a tech's test rig and extract critical files that way.
They sell two separate adapters which can be coupled to one another (in tandem) that connects the FW 800 port on your G Drive to the new imac's USB3/Thunderbolt port. There is no single adapter solution out there insofar as I am aware.
Look at the photos I've attached. One shows my old G-Drive with its FW800 output jack populated with my old adapter cable that came with the drive. The second photo shows the other end of that FW800 cable, and the two new Apple adapters lined up next to it. The first adapter is a FW800 to FW400 adapter; the second is a FW400 to USB3/Thunderbolt adapter. It worked for me, hope you can do likewise