It's not that GeForce has no VESA support. It's just spotty and/or shitty. 😀
If you were running this under DOS, I'd recommend you view this site.
http://unirefresh.demonews.com/videoproblems/
I know it mentions using VBEPlus to get the game running. But VBEPlus shouldn't work in Windows 2000/XP, and there are no comparable programs (yet) that do a similar thing.
Now, if X-Men uses UVBELib (they kinda give you instructions how to find out on that page, it sounds like it might too), then the UVBELib solution MAY work. You'd need to find out which version it came with, and use the right version. You'd probably still need NOLFB (search our forums), and even then, it may not work right.
IF you use the command "xmenpc.exe -u" it won't use UNIVBE at all. It'll be much slower, but it may work somewhat.
You _could_ try VBEPlus too, just to fool around. The only reason why is the author's comments:
Several users have reported that loading VBEPlus and/or UniRefresh solves the problems. I have once downloaded the 8bit version of XMen and confirmed that only after loading VBEPlus the game will run. (didn't matter what resolutions VBEPlus added, as long as it was loaded did XMen run well). I am not sure why this helps.
I'm not sure how VBEPlus works, maybe you could load it with no resolutions added at all - I'm not sure if resolutions HAVE to be added.
My personal solution to this problem would be to emulate the actual "X-Men: Children of the Atom" arcade game to play this, using ACE (Another Capcom Play System Emulator), Calice32, Final Burn, Final Burn Alpha, Kawaks, MAME, or Nebula. Sure, it may be different, but then you're actually playing the arcade game (but if you don't own the game and have downloaded the ROMs, it's quite illegal...)
If you break your PC trying any of this (although I'm not saying it's possible, I'm not saying it's not), I can't be held responsible. 😀
Let us know what you try, what works, what doesn't, and how you make out. 😀