Where does the term 'au pair' come from?

Compact OED defines it as "a foreign girl employed to help with housework and childcare in exchange for board and lodging", and says it comes from French for 'on equal terms'. Fine -- but the arrangement hardly seems 'equal', and the root seems to have nothing to do with being foreign or with being a girl.

What is the connection by which this french phrase came to be applied to this arrangement?

The intention is that the au pair comes to the new house as an equal, and not as a servant. The idea is that they are treated as members of the family. The fact that some people treat them as slaves doesn't alter that.

They generally come from abroad because they want to learn a foreign language.

And pair is related to our par and peer. The French word is from the Latin par which, in turn, is related to the words per 'through' and pro 'for'.