This was my first trip to France, and Paris was a great place to start the adventure. I thought I'd give some examples of things you can tackle in a day and still have time for a brief afternoon nap (or a rest for your feet,) and be back out for dinner. As I stayed in the 17e district, many of my suggestions begin there.
Day 1: Try spending this finding your hotel/apartment/rented flat from the airport. Enjoy your neighborhood with a nice walk. If you'll be traveling to other locations in France via train, then maybe take the Metro over to the main station and make your seat reservations (if required.) A nice dinner at a local restaurant is alway a great place to start. Get a good night's sleep.
Day 2: View the Arc de Triomphe then walk down Champs Elysées (do a bit of shopping) and hop on the Metro and take it to the Hotel de Ville. Step out and enjoy a carousel ride in the plaza (who can pass up one of those?!) I'd recommend visiting the Museum of Hunting and Nature (make sure to take your photo with the polar bear) and add a stop to see the Defender of Time (one of those fun little things we discover on our travels.) If you're up for some adventure then visit the Museum of Erotic Art over in the red light district.
Day 3: Spend the morning in Parc Moneacu - try eating your breakfast on a bench and enjoying the spring sunshine and doing a bit of people watching. Take a stroll through your neighborhood. Visit the Museum of the Middle Ages (plan for plenty of time to view the tapestries after you wait in line for admission.) Stop for ice cream on the Isle. Try dinner again somewhere new that's near where you're staying.
Day 4: Why not begin your day with a street market? Try one of the organic ones or venture into the Latin District. Then take tours of Sainte Chapelle and the Conciergerie (a joint ticket is your best bet for cost effectiveness.) When you're finished with those two take a walk over to Notre Dame. For your evening, walk/take the Metro over to the Louvre and walk across the Jardin to the Concord plaza just as the sun is going down. You'll be able to see all the way down to the Arc de Triomphe. Quite beautiful.
Day 5: Visit the Pere Lachaise cemetery to take a gaze at some of Paris' most famous dearly departed. This is also a great place just to walk and examine some of the tombstones and unique final resting spots. Then how about some impressionistic paintings over at the Orangerie? I'd suggest having dinner at Punjab and then walking over to the Eiffel Tower and taking a night time river cruise. (Make sure you sit on the outside of the boat for the best views.)
Day 6: Now this would be a great day to venture outside the city limits -
so why not a quick trip out to Versailles? It's amazing to see and a fantastic day trip.
Day 7: Reserved for the Louvre. Simply the Louvre.