Long time ago I had the problem that my old PC (Win7) started two instances of FF7 or was it that I need to start it two times to run the game. Anyway I had to open the task manager and had to kill a process (I guess it was run32.dll). Nowadays, I get slowdowns when my operating system was too long active, which easily happens because I play on a notebook. So a reboot can sometimes solve fps drops for me. I should also note that DLPB's Reunion mod comes with a new frame limiter (don't mix that with the 60FPS option), which also helps to stabilize frames.
BTW. the game performs differently in the different modules:
Field - 30 (FMV drop them to 15)
Battle - 15
Menu - 60
World - 30
The Rest - 30 or 60