What are the best secret things to do in Paris?

Go to "Jussieu" subway station . (Université Paris 6) go inside the university pick up an elevator, go to the last floor and enjoy a free panoramic view of Paris (possibly by night at winter). Don't get caught.

You have to try this restaurant: http://www.tripadvisor.co.uk/Restaurant_Review-g187147-d1866269-Reviews-Derriere-Paris_Ile_de_France.html There is a secret room inside a wardrobe. Really nice!

It's been a year since I've been in Paris and 5 years since I lived there, but, I can share with you some of my favorite activities: If you like underground places and good live music (jazz!) go to Le Piano Vache (8 Rue Laplace, 75005 ... Near Metro Cardinal Lemoine). Definitely check out the Japanese diners on Rue Sainte-Anne, 2ème arr. (that was my street!). The best one is Higuma (right on the corner of Rue Villedo). Sit outside the Centre Pompidou, at the fountain of Beaubourg. Real fun place full of all kinds of people. Go to the ÃŽle St. Louis and sit at the very end of the Island, on the east end. You'll see that the Seine River is very wide, almost like the ocean... Catch a movie at the Cour St. Émilion movie theater. Check out these parks:  Parc Des Buttes Chaumont (19ème) and Parc Monceau (8ème). Hope you enjoy the city!

Try Place Sainte Marthe in the 10th. Check out Chez Edgar, rue d'Alexandrie: nice café-restaurant on a hidden little place. Have an apéro on the piers of Canal St Martin (10th). You want to have a drink in rue Montmartre, in the block between Etienne Marcel and rue du 4 Septembre.

Though not exactly secret, you can try out any of these http://www.ixigo.com/horoscope-travel-signs-featuring-sagittarius-story-1106858 This is perhaps how you can change a normal trip to Paris to a fun one - You can start with putting a love lock on the Pont De Arts Bridge (check pic above), chasing the Holy Grail or enjoying a mug of coffee from the hard to miss Cafe Verlet. Shopping at the Saint-Ouen Flea Market or  Avenue Montaigne and Avenue des Champs-Elysées is also a great stress buster if you're ready to shell out some bucks.

If you're here for an extended stay, I'd advise you to start walking. Keep your eyes open. You'll begin to see things that the locals see. Pass through areas multiple times to get a clear view. Make friends among the French. They love their capital, and are (mostly) willing to share it with others if you have a good attitude.  Case in point; two nights ago I went to dinner with a friend in the Passage des Panoramas. We walked past three or four well appointed restaurants that my friend waved off with an elegant dismissal as "for the tourists." We went to the very end of the Passage to a hole in the wall that was last decorated about the time Napoleon returned from Russia. There, the joint was jumpin' and not a tourist in sight. The food was very good, plentiful, and, best of all, not expensive. The atmosphere was electric with tables of six, eight, or ten with everyone seemingly talking at once about très important, earth-shattering subjects. The bar was jammed with end-of-the-day-types drinking and talking as if the world's fate depended on it. It felt as if all of Paris was in that tiny spot. Frankly, without a guide, I could (and would) have passed on that place for months. But to do that would have extended my poverty, not that of Paris or the Parisians. Because they know. That place ain't never gonna show up on nobody's stinkin' website.

Illegal catacombs!  I mean, uh, don't break rules.When my friend took me shortly before I left during my year in Paris, it felt like one of the most surreal experiences of my life.  From sneaking over fences, a huge fire surrounding the two foot entrance (hole in the wall, I still don't know why it was there), to crawling through cramped holes I didn't know where I'd end up, it really was a test of finding out how willing I was to break my own comfort zones.  The scariest part for me was when we got to a stretch of tunnel where there was deep, muddy water.  We had to search with our feet for something to step on (some ledges along the side, some random parts toward the center) to go any farther.  Of course, I had no idea where I was underneath Paris or whether or not we were going to get lost and stuck forever (my friend had a hand drawn map, but he claimed to have been there many times =p).  If I was claustrophobic, I definitely would not have been able to get past the entrance!  Go to your local friends and ask them about it.  There are parties down there sometimes.  If you're not down for the scary parts, I'm sure there's plenty of other entrances that are safer!

You got already many excellent answers. Let me add: La Sainte Chapelle (near the Justice palace). It looks inisde like a miniature of the Middle Age La Mouzaïa, a promenade in narrow foot streets in Paris, near the Buttes Chaumont http://www.unjourdeplusaparis.com/paris-balades/promenade-dans-la-mouzaia rue du Moulin des Près (13 arrdt), lovely small shops and restaurants and bars The Mineralogic collection of the university P.M. Curie (UPMC Sorbonne Universités) http://www.collection-mineraux.upmc.fr/fr/index.html

Personally I love to go to the library Shakspear and Co, it's on of the jewels of Paris! Quiet place were you feel connected with the litterature and history. I love also to go Rue Mouffettard , one of the oldest street in the city, not far away from the ancient roman arenas of Paris.