Thanks to Ed Kurlyak for finding a way of changing aspect ratio and keeping the original vertical field of view without disappearing objects on the sides of the screen.

The executables are noCD.
If you prefer using the original one, follow these tutorials: 
https://www.youtube.com/watch?v=E_r0_IvE6Pk
https://www.youtube.com/watch?v=R0fMpJp8_IM

Setting a new resolution:
1. Go to Documents > EA Games > Need For Speed Hot Pursuit 2.
2. Open rendercaps.ini.
3. Set "LimitResolution" to 0 (if your screen resolution is higher than 1280x1024).
4. Change the values in the last two lines to your screen resolution (thanks to REDALiCE for this information).
5. Save changes.
6. Set your resolution in the game options.

Frontend folder contains HUD patch, which sets correct dimensions and positions for in-race HUD.
However, it also aligns majority of menus to the left and moves some text to incorrect positions.