Once you finalize with the Lounge that you will have access between your flights, you should consider and will not regret spending the entire layover there.

Where could you realistically go, outside the airport, with that little time, anyway? Six hours may well be a long(ish) layover, but also is definitely far from enough time to visit La Ville Lumiere. And you might indeed find it to be too little time for the Lounge.