1. Press Windows Key + R
   
2. Type "regedit" and select OK
   
3. Open "Computer\HKEY_CURRENT_USER\SOFTWARE\ubisoft\prince of persia\1.0\engine". You can also copy the path and paste it in the search bar on the Registry Editor
   
   
4. Double click "ScreenResolutionHeight"
   
5. Select the "Decimal" option
   
6. Change the "Value data" to "1440" and select OK
   
   
7. Double click "ScreenResolutionWidth"
   
8. Select the "Decimal" option
   
9. Change the "Value data" to "3440" and select OK
   
   
10. Double click "AspectRatioOverride"
    
11. Select the "Decimal" option
    
12. Change the "Value data" to "237" and select OK

And that's it!

Enjoy the glorious 21:9 resolution :D The menus and cutscenes aren't going to be in 3440x1440 but the game will (I'm still shocked at how beautiful this 12y/o game looks).
If you change anything on the launcher you might have to redo this.