Umm, the PS3 doesn't render PS1 (or PS2) games at 1080p. Or 720p. It renders them exactly as they were rendered on the original hardware. That's because (excluding the European PS3s and possibly the newer NA ones too), the PS3 contains the actual hardware from the PS2 (which contained the hardware of the PS1) to run the game. There is no opportunity to render at a higher resolution.
What it does do is upscale the image from the PS1's native (somewhere about 320x240, I'd guess, although the PS1 supported from 256x224 up to 640x480) resolution to whatever the output is.
The problem is, if you take a 320x240 image and upscale it to 1920x1080, it's just the original 320x240 image blown up. You can't create detail that isn't there. It doesn't really look any better. At best, you get smoother output, but no extra detail.
If you want high res FF7, the only option is the highres patch for the PC, which will render it at 1280x960. That's similar to 720p, except with a 4:3 aspect ratio.