Before we begin: Why doesn't CoD work with Windows 10?
The real reason why CoD doesn't work is that Windows 10 handles programs differently to other Windows versions. CoD doesn't work with Windows 10's DWM (Desktop Window Manager).
1. Download the CD-less fix
2. Install the fix
Go to C:\Program Files (x86)\Call of Duty and install the patch from the ZIP. Call of Duty Singleplayer will now work.