You cannot play PS1 discs directly on PSP. The PSP lacks a PS1 disc drive and native backward compatibility.
Legal Ways to Play FF7 on PSP/Go/Vita
PSN Classic (PSP/PS3/Vita): Buy Final Fantasy VII on PlayStation Store (PSOne Classic). Downloads to PSP/Go/Vita. Note: PS3/Vita stores closed July 2021; purchase via web store or PS3/Vita if still accessible.
PS4/PS5 Remake/Remaster:FFVII Remake Intergrade or original FFVII (PSOne Classic on PS4 via backward compat).
PC (Steam/Epic): Modern port with mods/boosters.
Switch/Xbox: Ports available.
Homebrew (If You Own the Discs)
Rip Disc 1 & 2 ISOs using a PC drive + ImgBurn / Redump method.
Convert to PBP (PSP format) using PSX2PSP / POPS Converter.
Install Custom Firmware (6.61 Infinity/PRO) on PSP.
Place PBP in /PSP/GAME/; launch via POPS Emulator (built into CFW).
Disc swapping: POPS supports multi-disc via disc change menu (L+R+Start) or combined PBP.
Legal: Only rip/convert games you own. Downloading ISOs/PBPs is piracy.