3 Days Itinerary

Day 1
Head first to the Eiffel Tower: morning (or late evening) is the best time to avoid the crowds. The most thrilling approach is via Champ de Mars.
Afterwards, tour the Seine on the Bateaux Mouches; these boats depart regularly from place de l'Alma.
From here, walk or take the métro to the Arc de Triomphe; from the top there's a great view of the boulevards emanating from L'Étoile and the noble vistas extending to the Louvre and La Defense.
Then work your way along the Champs Élysées, across Place de la Concorde and the Jardin des Tuileries to the Louvre. Don't visit the museum now - wait until the next morning, when it's less crowded.

Day 2
Get to the Louvre (closed on Tuesdays) early to avoid the crowds; in one morning you'll only be able to see part of the museum - it's that big.
After lunch, wander along the ritzy rue St-Honoré. Here you'll find the French president's home, the Palais de l'Élysée (closed to the public), and the Neoclassical Église de la Madeleine.
For good shopping and a look at Haussmann's 19th-century Paris and the famous Opéra Garnier, join up with the Grand Boulevards.
Spend the late afternoon getting a sense of Paris's village-like character by exploring Montmartre. Either walk (heading north along rue du Faubourg Montmartre to rue Notre-Dame de Lorette to rue Fontaine to place Blanche) or take the métro to the Pigalle or Blanche stop.
On boulevard de Clichy you'll find the famous Moulin Rouge.
Continue up into Montmartre, via place des Abbesses. On this square are two Art Nouveau gems: the church of St-Jean de Montmartre, and the Art Nouveau Guimard entrance to the Abbesses métro station.
From here, walk through the winding, hilly streets to place du Tertre, and then on to Sacré-Coeur, where there's a tremendous view of the city below.

Day 3
Start the morning admiring the Impressionists in the Musée d'Orsay (closed on Monday); arrive early to avoid the crowds. Then head to Notre-Dame Cathedral, perhaps the most inspiring monument in Paris.
In the afternoon explore the Latin Quarter, using the Panthéon dome as a landmark. Take time to relax in the Jardin du Luxembourg or sip coffee in a neighborhood café.