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Welcome lilniffa
Salut et bienvenue lilniffa! Welcome to Flyertalk and to the BA board, thank you very much for that very informative contribution, and may we see plenty more of you here. Welcome to the forum!
I've struggled with this question, since I like Paris so much that 6 hours is borderline insulting in my opinion. But having thought about it, my suggestion would be to go as far as Châtelet les Halles on the RER, then walk - perhaps deliberately without a map through to Île de la Cité - look at Notre Dame from the outside - then on to the romantic treasure of Île Saint Louis that no one seems to visit. Then head north to the Marais for a more buzzy streetlife, then jump on to any random Métro station back to the airport.