Right-click on your desktop, click "Properties," "Settings," "Color Quality," "Medium - 16 bit."
Though it won't do anything. Final Fantasy VII automatically reverts to 16 bit color, anyway, unless you have the 32 bit patch applied, which I'm doubting that you do.
I guess it might have some effect. The high resolution patch won't work on my computer unless I set my resolution to 1280x960 on the desktop prior to playing the game. It will automatically go to 1280x1024, if I have that part of the patch applied. I don't know if that's a common problem; I mention it, though, because maybe setting your desktop to 16 bit color could help.
If nothing else, run the game in Software Rendering. I hear it isn't quite like Hardware Rendering, but at least it should work.