I got Rayman 3 installed an running using wine 1.2.2 on linux mint (ubuntu) . I haven't gotten too deep into the game but so far it seem to be working just fine.

Rayman 3 installed fine on my Archlinux using PlayOnLinux, but when running it, the game crashed after collecting the first 6 red lums. Setting the Wine Version to 1.2.3 solved the issue.

Haven't played far yet, so maybe ther will be problems later...

I have now played through the entirety of the game without any issues.