I also have this issue, PS4 hardened edition.
Free Fall was working fine up until the latest patch was released.
Now, no DLC works so I can't download the Festive camo either.
It knows Free Fall is installed as it comes up as a map to play in Local Play, but loading it has the grid loading screen.
What do you people have in your Library on the PS4? I have two entries for COD. One is blank saying 3 add-ons and one has the COD image with 4 add-ons. In addition to that I get 'No Content Found' on the PS4 home screen.