There are literally more than 100 churches that can usually be seen for free. You should go to Sacre Couer in Montemarte, St. Sulpice, St. Germain de Pres, Basilique de St. Denis...and there are more. To help pay for restoration please drop some money in the boxes for the restoration funds. Also, Notre Dame is free to walk around in, but with your Paris Museum Pass you can take the walking tour with the headset (I always recommend the headsets around 5€) and go on the extra tour which includes the churches most precious relics. It was very impressive, even for someone who wasn't sure what a relic was... Another great church, to be seen on a sunny day is St. Chappelle. I would take some opera glasses, and maybe a copy of the old testament the next time I go, and could sit for hours looking at the amazing stained glass stories.
If you like tour busses, and especially if the weather is nice, the hop-on-hop-off bus systems are very good here. L'Open Tour has a two day pass for 28€ that allows you to see quite a bit of the city. There is a red bus that has a similar service. There are also boat tours on the Seine that are really excellent. Get the boat down near Notre Dame, and particularly during the evening, that ride is beautiful.
The tour books also help you with the enormous task of seeing the Louvre. There is a great DaVinci Code Walking Tour book that walks you around the Louvre to the sights mentioned in that book. Rick Steve's also has a walking tour of the Louvre in his book. Of course, you could just wander around until you find cool things -- they are everywhere.
At the Louvre right now there is a special exhibition by an artist named Ingres. It costs extra, and if you have a Carte de Musee you can cut the line. On Monday mornings the line is not so bad. It is an excellent exhibit. Louvre is closed on Tuesdays and is open late on Wednesday nights.
At Musee D'Orsay there is an English speaking tour at 11:30 a.m. Tuesday through Sat. that is supposed to be very nice. I have not taken it yet, but plan to. The Musee d'Orsay is closed on Mondays. There is an awesome restaurant on the top floor with reasonably priced meals, and a more casual, but not with such a great view carry out place above that. You have to go see the Van Goghs at Musee D'Orsay, and the impressionists are impressive, too.
The old Opera House, near Boulevard Haussmann is an excellent site as well. The inside is really beautiful and you can just imagine yourself floating up the grand staircase in your finest finery. There are english speaking tours at 11:30 and 2:30, though I would double check that. It is not covered on the Musee Pass and I think the tickets were €8 for the self-guided tour.
A nice day trip is the Chateau Versaille. The one day pass is 20 €, gets the headset and entrance to the special exhibit and gardens. The Paris Musee Pass works here, too and lets you cut the line. You take the RER C5-train from Paris for about €6 round trip.
I also recommend a trip to Haussmann St. the shopping store mecca. Go the 7th floor of Gallerie Lafayette for this amazing view. At Christmas it was gorgeous. It is the home of the big retailers. You will also go to Champs Elysees to see the Arc dé Triomphe and sing Joni Mitchell, but you will see plenty of retail there. If you aren't tempted to shop, both of those trips could be free -- but I doubt it. Sit in a café and keep humming... I was a free man in Paris, I felt unfettered and alive...nobody calling me up for favors and no one's future to decide...
I also loved our adventure to the Musee du Vin and the wine samples afterwards, though some others thought it was too hokey. Just this week I saw a Renée Magritte exhibit at Musée Maillol. There is also the Rodin Museum, which I haven't been inside yet, and Hopital Invalides with Napoleon's Tomb and war museum. It is interesting and especially if you are into horses, war things or military dress kind of stuff. They display Napoleon's horse and dog, stuffed for perpetuity. I think there is a Stephen King novel about what a bad idea that is.
Now with all that (and that is a small piece) --- don't forget the best part! Strolling along the Seine or Champs Elysee and sipping thé in the streetside cafés or prowling through the book vendors carts you will just love it, especially if the weather is good. For .90 centimes you can get the best bread you have ever eaten at any patisserie. There is some justice Cokes are €4 but coffee is about €2 and Vin rouge is usually less than sodas at most cafés. Leave time in your plan for watching the occasional ptonk game or sitting in the sun on the steps of the Opera, or just marveling at how they drive through the roundabout at the Bastille.
I would go back there tomorrow, but for the work I've taken on...
