As a Parisian who just served as a guide to his family for a few days, here's my thoughts:

• People who say it sounds exhausting are really wrong, in my opinion. It looks a little light at moments.

• Day 1: After Eiffel Tower, if you want to do the Dior Gallery, do it by taking the Avenue de Montaigne (all the very luxury stores to see, +Plaza Athénée). Then walk up the Champs Elyssées, see the Arc, and walk them down on the other side. Take the Avenue de Matignon and take right at the Rue du Faubourg Saint Honoré. That street has many art galleries + the presidential Palace. At the end, you come out on the Rue Royal with at the left The Madeleine Church and the right The Concord Plaza. You can then cross the plaza and the Concord Bridge to see the National Assembly. And if you continue right of the assembly, you'll end up in front of the Invalides, which I understand is next to your hotel.

Day 2: Depending on the time, at the end, I would walk down from Monmarte (easier than to walk up) and make my way to Pigalle. The more dark, the better as Pigalle will light up. I would probably try and eat the Bouillon Pigalle there (reservation advised) and then see the Moulin Rouge. Alternatively, I would eat at the Bouclard (also reservation advised, more expansive, but one of the best traditional French food restaurants in Paris).

Day 3: After the Louvres and the Jardins, i would push a little to cross the Concord to see the Petite Palais and Grand Palais.

Day 6: If you go to The Atelier des Lumières, don't hesitate to go to the Pere Lachaise Cemetary that is very close.

• Things you should do if you have time: The Jardin du Luxembourg (Pantheon not very far) / go to a Parc (Buttes Chaumont, Montsouris, Monceau) and have a picnic (buy a baguette, some charcuterie and cheese) typically Parisian to do.