When you have this kind of layover the key is to be very selective. What is your dream of Paris? Do that one thing and have a nice dinner (book ahead) and then after dinner take a stroll around Notre Dame after dark -- it is one of the great sights in the world. Perhaps have a drink with a view or do a Seine Cruise (there is a boat that launches under Pont Neuf which is fairly close to getting back to St. Michel Notre Dame and the RER B to the airport. ) Or you might want a long leisurely dinner and that stroll and then to hop on the RER B nearby. L'Initial which is quite close to Notre Dame is excellent and their 48 Euro tasting menu is wonderful. We paid nearly as much for dinner for much less at Rotisserie La Tour d'Argent also nearby. (this is the 'cheap' sister to the very pricey La Tour d'Argent next door). There are also brasserie on Ile St. Louis where you could have a meal and be in a pretty part of Paris. You could buy a bottle of champagne and drink it down by the water on Ile St. Louis. Be discreet with bottles; technically not legal but in the category of everyone does it and if not rowdy no harm no foul. The views are just beautiful; a very romantic way to end a brief Paris visit.
We had a similar layover in London one time; AA forced us on our own nickel to stay overnight but would not allow us to break the trip there for several days. We were at a hotel at Victoria station at about 5 pm. We had fish and chips in a pub and then took in a Gilbert and Sullivan performance at the Savoy and then took an evening stroll across Westminster Bridge which was stunning at night. We got the. Gatwick express at Victoria station to the airport the next morning. It was a laid back fun little bite of London. Less is more when you have little time -- do something that you can savor.
With a noon flight you could easily stay in the city and take a cab or train in the morning and be there by 9. but booking a hotel AT not near the airport like the Novotel for example or Ibis, leaving your stuff and then doing into the city by train for the evening would also be sensible.