Alternately, you could not bother with these strange programs and get a controller that works. I'm currently suggesting any of the 8bitdo series (currently sold on Amazon), that way you can have a controller that works 4 ways.
Most of the Rayman series was made before Xinput was even a standard, so using any Xinput device is just going to throw hoops into the mix.
A bit of a late response, but I wouldn't call AntiMicro a "strange program" considering that it's one of the few free and open-source alternatives to the likes of Joy2Key and Xpadder, at least to my knowledge.
Plus, I doubt the topic creator would want another controller, let alone having to fiddle with an 8Bitdo controller to get its D-Pad to not accidently cause unwanted diagonal movements.
I also have an Xbox 360 controller but I play R2 with my keyboard. May I suggest you to try out this? https://www.mediafire.com/file/z5geoudy9iu9ova/Rayman2InputFix_v1.zip/file
I wouldn't recommend that one, since experience tells me that the jump button is mapped to the B button instead of the A button, at least on my 360 controller, but if that doesn't happen to you, then kudos.
If anyone were to play R2 on keyboard, I'd suggest using DINPUT Key Switcher
to remap R2's default keyboard layout.
Though honestly, you're kind of better off emulating either the Dreamcast or the PS2 version instead.