I will try to answer some of your questions.
Assuming the flight is on time, by the time you are out the door, it will be 10 pm or close to that.
If you really want to enjoy the city, I would take a taxi from the airport and go to the hotel. The city is large and you will not see significant amount of it by foot in one night.
I would ask the taxi to do a small tour for you.
Ask him/her to do Monmartre, Tour Eiffel, Champs Elysee, Arch de Triomphe, Louvre, Place de la Concorde; go by the Opera Garnier, Bastille and then to your hotel. This will give you an idea of what the city looks like.
I would look for a hotel in the 6th arr. It is a great area to hang out at night and you will find plenty of things to see and open restaurants at night.
If you want to continue seeing stuff, I would wake up at 6 am, go to a cafe, have a bite and then go out for an hour walk around the river. Go to Notre Dame and walk to the Luxembourg gardens.
I would take a cab back to the airport. Getting out of the city on a weekday takes a long time. I would plan on leaving 2 1/2 hours before your flight; give yourself 1 hr for the trip to CDG and 1 1/2 hours before your flight.
I guess AF will allow you to check the luggage through.
I don't know if you are flying coach, business or first. if you are going coach,
AF is good. Being Elite Plus they treat you nice at the airport. You can use the business class check in area and use the Business lounge if you want. Food is acceptable and service is professional and efficient. Still serve champagne on international flights in coach.
I would try this restaurant in the 6th arr
Le Procope:
http://www.procope.com/
Hotels are expensive but try this one:
Best Western Left Bank-St. Germain - unbeatable location.