Sacre Couer-- great photo spot, very romantic
Walk along the Seine by the "New bridge", which is actually Paris's oldest bridge.
For great art, visit the art market in Montparness on Sundays.
Try to see at least one museum, but don't try to see them all. Pick one and try to savor it, rather than rushing through.
Check out the Catacombs for an unusual experience.
If you're choosing one church to see, I'd recommend St. Chappelle over Notre Dame. Truly more beautiful, smaller and less crowded. (Also, not near the hike to the tower.
Quick Tips:
Here's our "tip list"
In March, make sure you pack gloves, a scarf and a hat. Also, an umbrella. We found the weather unpredictable and changeable. We also wore thin long underwear on most days, to make being outside more enjoyable.
Learn the metro system, and buy (or at least research) a Carte Orange for travel on the metro. (We saved a TON of money on this weekly pass)Under no circumstances would we advise driving in Paris!
Try to go with the fixed price menus--not only do you save money, but they offer great variety and are often the chef's special.
Many musuems/attractions are closed on Sunday and/or Monday, so plan your trip accordingly. Don't save your #1 activity for a Sunday, unless you're sure of the hours.
Plan on some late nights. Most restaurants don't open for dinner until around 7:30, so bedtime is often late, as dinner can take three hours!
Best Way To Get Around:
METRO, METRO, METRO. I can't say it enough! Cheap convenient and easy!
Although, you also need to make sure to get out and walk around!