Forest Preserve outside city radius?

[Tavenier]

I know the benefits of forest preserves. But outside the city crosses does it still pay off to have them? I know it increases the chance of spreading forests/jungles into adjacent squares, but does it also have a positive effect on your city happiness? Or your empire as a whole?

 

[oranges]

AFAIK, there are no other benefits outside the city cross other than increased chance of forests spreading

 

[Refar]

To gain eny benefit (Happiness, Healtt, Free Great People with NP) the Forest/Preserve must be in the Cities BFC.
Preserves outside help only with spreading forest