The North American version of this game is called FIFA Soccer 2004, and the European versions of this game are called FIFA Football 2004, so I'm titling this post FIFA 2004 for simplicity.
This one works mostly the same as FIFA 06, so setting it up was pretty easy. This game is a bit quirky though: Each profile is saved to a separate gci (in which the exploit uses the first one, which is profile0), and having multiple profiles on the memory card will cause each one to be loaded individually before the exploit occurs, so it is better to not have any other profiles on the memory card when using this exploit. Additionally, the Eurpoean versions are even more quirky: if you have profiles on the memory card from different versions (such as having profiles from the French and Italian versions), then all of those will also be loaded individually before the exploit occurs, even though the game doesn't allow profiles from other versions to actually be used.
The repo can be found here, and the gci files can be found here.
And here is a video of the exploit being used to load Swiss.
FIFA 2004 Save Exploit
FIFA 2004 Save Exploit
TTYD Speedrunner