PLAN NOW, LONG BEFORE YOU GO....
Here are some suggestions of things to see and do, grouped by proximity to one another and by day. Keep in mind that this is just a short list, and is only a sample. You should be thinking about what you would like to see, and plot an itinerary now. If you don't and you just go, you may miss some things and regret it later. Keep in mind that some things may be closed on certain days. You should check out all of your destinations on the internet to see the hours and days that they are open. Use your guide books to help you plan. Start reading NOW. An excellent one that I will be using is Access Paris, by Richard Saul Wurman. You could have Mendocino Book Company order it for you, or you could order from Amazon.com.
Quartier Latin and St. Germain des Près--Walking tour rather than Metro
Quartier St. Germain--Go to Place St. Germain des Près, have a coffee in famous cafés (Aux Deux Magots--facing l'église, Café de Flore, on the Boulevard St. Germain), walk down the rue St. André des Arts behind the church in St. Germain towards la Place St. Michel. Latin Quarter--5th arrondissement--Walk around St. Michel Area--Bookshops--Rue St. Jacques and walking area off of Place St. Michel--Musée de Cluny (from the Middle Ages), Visit Pantheon and area behind it--Lovely Place de la Contrescarpe, market area of La Rue Mouffetard. From St. Michel Area
Day Two
Les Deux Îles and La Samaritaine
Metro--Direction Porte de Clignancourt (line 4), get off at Cité. Wander around Ile de la Cité and Ile Saint-Louis, check out----Notre Dame, Berthillon Ice Cream/Sorbet on the Ile Saint Louis, le Marché aux Fleurs on Ile de la Cité, 16th century mansions (hotels particuliers) on the Ile Saint Louis. Cross to the Rive Droite and walk North-West along the Seine until you reach La Samaritaine Department Store. Cross back to the left bank via the oldest bridge in Paris, Le Pont Neuf (the New Bridge). Be sure to look back to the Northwest for a good view of the Louvre.
Day Three
Le Louvre, Le Palais Royal, Paris Chic
Metro--Direction Porte de Clignancourt (line 4), transfer at Châtelet, then direction Pont de Neuilly (line 1), get off at Louvre. Louvre--devote a morning or afternoon to it, enter directly from metro station---Le Palais Royal behind the rue de Rivoli---Place Vendome, Rue de Rivoli and environs ((Ritz Hotel--be sure to see one of the original Meters embedded it the wall, Cartier, Yves St. Laurent, Chanel, Pierre Cardin, Godiva Chocolatier, other fancy shops)
Day Four
Shopping at l'Opera, Champs Elysées, Arc de Triomphe, Eiffel Tower, Bâteaux Mouches
Metro--Direction Porte de Clignancourt (line 4), transfer at Strasbourg-St. Denis, then direction Balard (line 8), get off at Opéra. Opera district for department stores (Le Printemps and Les Galéries Lafayette), les Champs Elysées, l'Arc de Triomphe, la Tour Eiffel, Bateaux Mouches at le Pont de l'Alma on the right bank.
Day Five
Le Musée d'Orsay, more St. Germain and Latin Quarter
Metro--Direction Porte de Clignancourt (line 4), transfer at Châtelet, then direction Pont de Neuilly (line 1), get off at Tuileries, walk across the Jardin des Tuileries to the Seine, walk across the Pont Royal, then North-West along the Quai Anatole France to the Musee d'Orsay, Dégas, Cezanne, Van Gogh, Monet, Manet, Renoir, Gaughin, they are all here. So is Whistler's mother. Explore more of the Latin Quarter and St. Germain (5th and 6th).
Day Six
Montmartre, la Place des Vosges, le Marais, le Centre Pompidou, Forum des Halles
Bus to Montmartre--Wait at stop somewhere between the Luxembourg Gardens and la Place St. Michel on Boulevard St. Michel, on side headed towards the Seine. Make sure that bus number 85 is shown to stop there. Take number 85 (direction Mairie de Saint-Ouen all of the way to the stop Rochechouart-Clignancourt (or thereabouts), walk up to Le Sacré Cœur on rue Picard. Make sure to go to la Place du Tertre (touristy square but lots of fun) behind the huge white church of le Sacré Cœur. Also, don't forget to see the gorgeous view from the steps in front of le Sacré Cœur. You can also take the mini-train for a tour of Montmartre down to la Place Pigalle (where the Moulin Rouge is). For la Place des Vosges, le Marais, le Centre Pompidou, Forum des Halles, return via bus 85, direction Luxembourg. Get off the bus at Coquillières-Les Halles and explore le Marais and others on foot all the way to the completely enclosed Renaissance square called la Place des Vosges. Make sure to tour Victor Hugo's home and museum on the square if you have time.
Day Seven
Versailles
Take RER line C from St. Michel-Notre Dame Station--Direction Versailles-Rive Gauche, you will have to buy special round-trip tickets at the RER station ticket window. From the Rive Gauche station in the town of Versailles, go right on Avenue de Gaulle, then left on Avenue de Paris. The chateau will be in front of you. Make sure to walk in the gardens behind the chateau (free) and visit le hameau (hamlet) of Marie Antoinette.