So before making this post, I'd like to mention that I've done a fair amount of research before writing this. I was able to get the controller support working in Rayman 2 by copying over the dinput.dll file via the InputFix and that got my controller working again, however there's an unusual issue I honestly wasn't expecting to run into.

The game seems to be completely reversing the state of the Left-Trigger, which means I'm stuck in strife mode unless I hold it in. Very uncomfortable for long-term play, especially since I have a bad left wrist.

I'm using Windows 10 with an Xbox One controller, everything is calibrated correctly and works fine in everything else. Naturally, my version is the one you get via GOG and I downloaded it via the GOG Galaxy software.