By using
GCMM on a homebrew-enabled, Gamecube-compatible Wii, you can back up your Gamecube saves to SD card. F-Zero GX used to give people problems because its saves used some sort of protection, but the latest GCMM supposedly has the capability to rip them successfully.
After you back up your saves, you can put them into your Nintendont memory card file on a PC using the Dolphin emulator's memory card manager. I've done it myself, it worked with everything I've tried so far! Though I haven't tried F-Zero GX...
If you've tried and are having trouble, I could write up a more thorough explanation!
EDIT: Gbatemp's Nintendont compatibility page says that memory card emulation isn't working yet for F-Zero GX. Anyone tried? I don'y have the game so I can't test.