I've been experiencing some problems with Beyond Good and Evil for the PC.

It seems to happen at certain places (Leaving a room, starting the first looter race, approaching a large whale creature) that my PC will just throw up a BSOD and restart.

I'm running Window's XP SP2 Home Edition, 512 RAM, GeForce FX5200, and a 1.8ghz processor.

It gives the following error..
"STOP : 0x0000008E (0xC0000005, 0xF7802675, 0xB9EDD204, 0x00000000)

smwdm.sys - Address F7802675 base at F77DD000, DateStamp 3cacal64"

Any ideas on how to fix this?

It's your sound card driver causing the BSOD, try updating it.