What family is the french horn in brass or string or woodwind or purcushin?

Horns are actually mid-range instruments. They're dead center in the spectrum of brass instruments: lower than trumpets, but higher than trombones and tubas. They often share super similar parts to alto saxes in concert band repertoir. However, horns have quite a large range because of its conical (cone) shape, and aren't restricted to a set range like trumpets and trobones are.

Hope this helps! =)