1. Go to the Louvre. Skip the most famous pieces, the Mona Lisa and the Venus de Milo - or, if you must, run past them just so you can say you were in the same room as them. (Watch this video to see how it should be done in maximum, floor-sliding style.) Instead, go to the Dutch and Flemish paintings to see works of Rubens, Rembrandt, Vermeer, Ruysdael, and others. Particularly impressive is the Medici room, a series of 21 paintings by Rubens depicting the life of Marie de Medici, the wife of the French king Henri IV, and mother of Louis XIII. Spend as much time there as you can stand, and then go out into the Tuileries and sit down for an ice cream cone, and then a glass of wine and a sandwich at one of the outdoor cafes.
2. Go to the Shakespeare & Company bookstore, just over the bridge from Notre Dame Cathedral, on the left bank. Go up to the second floor, grab a book from the shelves, and find a chair or couch in a quiet corner to read it. (This is not only tolerated, but encouraged - in fact, most of the books on the second floor are not even for sale.)
3. Go to a cemetery. Pere Lachaise is the famous one, with Oscar Wilde and Jim Morrison, Piaf, Proust and Chopin; but the Montmartre and Montparnasse ones also have loads of famous dead people (including Hector Berlioz, Francois Truffaut, and Louise Weber, aka the can-can dancer "La Goulue" in Montmartre; Sartre, de Beauvoir, de Maupassant and Susan Sontag in Montparnasse). Just make sure you have a good map of the cemetery and the notable graves in it before you go. They are not neatly, geometrically arranged places; there are acres and acres of tombs and gravestones, many of them old, faded and mossy, often hidden behind large sepulchres of long-forgotten aristocratic French families, and few pathways through them.