We just went last week and spent 8 days in Paris. Based on our experiences here's what I would suggest:
Day 1: Notre Dame, San Chappelle (it's right by Notre Dame. It's almost entirely made of stained glass and amazing), Cluny Museum (also in the same area). We did all three in one day. Stroll along the Seine.
Day 2: Louvre (either know what you want to see ahead of time- this place is HUGE or book a guided tour. We used Art Journeys Paris and thought it was money well spent), Arc de Triumph, Eiffel Tower. We prebooked our tickets. Stayed for the sunset and then walked over to Trocador for an awesome nighttime view of the Tower. Had ice cream and enjoyed tower sparkling at the top of the hour.
Day 3: Paris Walks has some very affordable and interesting walking tours (I think it was 15euro each). We did one that took us around Montmarte and then ended at Sacre-Coeur. You could head over to the Rodin museum afterwards. Orsay museum is also close to Rodin.