You have to check your system performance, here are the Fallout 3 system requirements:
Recomended
3 Ghz Intel Pentium 4 or equivalent processor
1 GB System RAM
ATI X800 series, Nvidia GeForce 6800 series, or higher video card
Minimum System Requirements:
* Windows XP
* 512MB System RAM
* 2 Ghz Intel Pentium 4 or equivalent processor
* 128MB Direct3D compatible video card
* and DirectX 9.0 compatible driver;
* 8x DVD-ROM drive
* 4.6 GB free hard disk space
* DirectX 9.0c (included)
* DirectX 8.1 compatible sound card
* Keyboard, Mouse
I have this game too and it runs fine with my 32bit Windows 7, I didn't have to do compatibility mode either or Administrator mode.