Morning
Head first to the Tour Eiffel (M° Tour Eiffel, Pont de l'Alma): morning 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 (M° Charles de Gaulle Etoile); 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 Défense.

Afternoon
Then work your way along the Champs Élysées, across Place de la Concorde and the Jardin des Tuileries to the Louvre.
Get to the Louvre (closed on Tuesdays) ; in one afternoon you'll only be able to see part of the museum - it's that big.

Evening
Go to the Moulin Rouge on boulevard de Clichy you'll find the famous Moulin Rouge (M° Place de Clichy or Blanche).
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.