Wow, that's a really sneaky "false friend" in Italian! Especially since it even has the meaning of "forest-related" in other Latinic languages, e.g. in French route forestière = forest road.

I wouldn't call it so much a false friend as forest/foreign (and forfeit and I'm sure a bunch of other words) all coming from the same Latin "foris" root and being semantically related.

In Italian, outside is just "fuori".

You're a foreigner to what you've forfeited in the forest.

Forest-related is "forestale" in Italian.