Montmartre is enchanting. (Think of the movie, Amelie.)
At the foot of the steps, across the street, is a little street cafe with outdoor seating.
Sit there. Get a cappuccino and a croissant.
Sip your coffee. Tear off small bites of your croissant.
Watch Paris flow by you. The tourists. The locals. The delivery boys.
Have another sip of coffee.
Do not set a schedule or a time limit. Just be. And take it in for a while. It will be deeply affecting.
Any time you happen to be walking anywhere, and feel a little hungry, look for one of the little neighborhood restaurants that are below street level. Doesn't matter where. Walk down the steps and into ... Paris. A waiter will seat you. They don't speak English. You don't speak French. But it won't matter.
Get the house red wine, and whatever the special is. Giving ourselves fully over to experiences, without planning, pretense, or expectations is generally the way to have the most amazing and memorable (and romantic) time.
Enjoy. There are plenty of reasons why the simple mention of Paris brings peoples' emotions to the fore. Go with it. Let Paris happen to you, and you will have an amazing time.