DirectX/FF7

No clue.
__Square has a tendency of being tight lipped about their game development. Most likely you would have to ask them directly, though there are a few ex-Square programmers out there.
__My guess would be a C variant since they practiced their 3D programming on an SGI workstation.

I would also think that it would have been done with C+Asm. You know... what most games are made in.

Yeah, I heard it was a C variant as well but, as said above, you'll have to look darn hard to find info on it. I've actually been quite amazed how tightly the console folks have been able to lock down info their APIs and code. You want to do something like it, you're best bet is just to sit down, study it, and attempt to black box the engine...

__Personally, I wouldn't try too emulate the PC version *perfectly*. There were many Lighting and texturing bugs compared to the PSX version. Plus the engine still requires very good graphics cards to display a nice image. Some of the newest cards still choke in areas of the game.
__Still, it could serve as a good template for games that use 3D characters with 2D backdrops and UI.