For the prequel, see Need for Speed III: Hot Pursuit. For the 2010 game, see Need for Speed: Hot Pursuit.
Use the DirectInput FPS Fix.
If the above doesn't work (it didn't on my Windows 8.1 x64):
Hot Pursuit 2 suffers from frame pacing issues on modern systems, resulting in choppy gameplay even at high framerates. There is no known fix for this.
Even after setting "World Detail" at maximum, the game won't render fog on modern systems.
Go here and download the d3d8.dll and place it in Need For Speed Hot Pursuit 2 folder and the d3d8.dll will load d3d8to9 and convert DX8 API calls to Direct3D 9 ones.
This issue can be fixed by installing HP2WSFix as the fix is integrated along with the widescreen fix.