That's very odd, I didn't have to do a single thing at all to get it to work. Have you tried playing another game real quick to make sure the controller is working properly and that it's just FF7 that's the problem?
I have the same trouble. I ended up just mapping everything through xpadder after about 15 minutes of exiting and relaunching the thing. It's weiird because it works fine in the launcher when changing button mappings, but the game just refused to acknowledge the 360 controller.
I thought about unplugging my other two game input devices, but I'm of the mindset that I don't make changes to my computer set up just to get one game working...and xpadder worked fine.
Also, not sure if anyone else has commented on the OGG PSX music that was so kindly shared here, but the LoopStart=0 on yado.ogg (the inn music) loops indefinitely for me at the part of the game I'm in now, first time using an inn, so I'm not sure if other inns would have looped endlessly or not, but removing that loop tag fixed it. I feared I'd have to go back to the updated music, which is absolutely atrocious in the Slums area that I'm in.