For the end of our honeymoon, my fiancé and I were going to spend a long weekend in Paris. We are starting our honeymoon in Iceland, then hiking in the Alps, and flying out of Paris. We plan to visit the Eiffel Tower, the Louvre and go shopping. Are there any other museums or must sees in Paris you would recommend going to?

Paris has so many wonderful sights so many but I don't know your interests. I suggest looking at a guidebook to get a sense of all that Paris has to offer and what you might enjoy.
My favorites include:
Notre Dame Cathedral
Sainte-Chapelle
L'Orangerie museum
Musee D'Orsay
Renoir Museum
Luxembourg Garden
Strolling Rue Mouffetard

You and your finance certainly seem to be traveling a lot this year!

Personally, with only 4 days (I assume that means 5 nights?) in Paris, I would not make going to the Eiffel Tower a priority -- seeing it, yes, going to it, no. JMO.

More to the point, I don't think anyone can give you reasonable advice without knowing more about why you and your finance have chosen Paris. Have you looked at any guidebooks? That would seem to me a good place to start.

Congratulations, best wishes, and happy planning!

2 suggestions:

Les Puces de St Ouen: a sprawling collection of a dozen flea markets that are a riot of color, objects, jewelry, and antiques. Everything from an 18th century carriage to a suit of armor to vintage mailboxes. Best visited on a Saturday or Sunday morning.
https://www.tourisme-plainecommune-p...0#lg=1&slide=0

Climb the spiral stairs and walk along the rooftop of Sacre Coeur. Few people seem to know about this. You will probably be alone up there.
https://www.sacre-coeur-montmartre.c...the-dome-tour/

I didn't go up the EIffel Tower until my 8th trip to Paris, and then I wondered what all the fuss was about.

Rather than go UP the Eiffel, have a dinner near the Seine, then take a Batobus boat ride down the Seine with arrival time at the base of the Eiffel of 9:00 PM, or 8:55. That's when its light display goes off. Romantic. Tell the new wife that THAT'S what she means to you. ......;the rest is up to you.

In addition to other suggestions I'd suggest checking out the Rodin Museum, Versailles, the Catacombs, the Pantheon, the Conciergerie (where Marie Antoinette was held prisoner), the Maison de Victor Hugo, and the opera house too--but that's just going off my own interests! The Shakespeare and Company bookstore and the Grand Palais/Petit Palais are great to stroll by, and the nighttime view of the Eiffel Tower from the Pont Alexandre III bridge can't be beat.

Also, right by the opera house, the Galeries Lafayette Paris Haussmann department store has an amazing rooftop terrace which at least used to be free and open to tourists--wonderful view of the city.

Both Gallereis Lafayette and Printemps department stores, near each other, have these amazing Art Nouveau domes, among the visual highlights of Paris.

With just 4 days, no one could possibly see all the suggested places in this thread (or in any guidebook, for that matter). The OP mentions one museum (the Louvre) that could take up the entire 4 days, The best plan would be an introductory skim of a few essential sites and some seat of the pants wandering, which seems to be the OP's idea.

It would be possible to add one more big thing. Another art museum? Cluny Museum of the Middle ages? The Picasso museum? The Orangerie? The marvelous stained glass of the Sainte-Chapelle? Or any of a zillion other famous places? How about a guided walking tour? Or the Fat Bicycle tour? Or a half day view the sights orientation bus tour? Or visit Fragonard's perfumery? Or walk around in the Botanic Garden? How about going to the top of the Tour Montparnasse around sunset to see the illuminated monuments including the Eifel Tower all from one place? Or an evening bus tour to see the same?

You can't do everything but you could try any one of them. And then come back another time to do more.

When the OP asks for your own 'must-see' places, I assume that means places you are passionate about. If you are passionate about visiting the Perfume Museum, then of course let the OP know. I though it was only ok.

Thanks! I will look into that. I think that would be really cool to see

Thanks! We will look into that. I think that would be really special at the end of our honeymoon.

Thanks! We will check out the walk on the spiral staircase. We love doing stuff that is non touristy to avoid crowds.

For shopping I would skip G-L and Le Printemps and take in Le Bon Marche in the 7th I like the lines they carry much more, and the area in front of the store (Rue de Sevres I believe) has great shops not seen in G-L and Le P. I would also skip the Louvre and go to a smaller museum aligned with your art interests: d'Orsay, l'Orangerie, Rodin (sculpture near ET), Carnavalet (history of Paris, free, fascinating). I would not go to the flea mkt mentioned above on this trip, you're likely to find things that are cumbersome and a problem to get home -- it is huge and not easily found/reached. I suggest using G7 if you need Uber-style fabulous service if you choose not to Metro -- get app for your phone and you're good to go. Would strongly recommend staying in St. Germain de Pres, the 6th arr. It is quiet, charming and oldest church of Paris is there -- shops there very good too.

The Luxembourg Garden is the perfect place to relax, have a picnic, and enjoy the romantic setting.

Bon Marche is a bit interesting looking, though not when you compare it to the Grands Magasins. The domes inside Galleries Lafayette and Printemps are simply jaw-dropping.

As far as Les Puces is concerned, the OP is not obligated to buy anything. It's an astonishing area just to see. And jewelry is not cumbersome to get home if you do want to buy something.

For the OP: If you do go to the Louvre, here is my hot tip: Le Cafe Mollien on level one has a balcony with a spectacular view. You don't even have to eat there to enjoy the view.

For something romantic and unusual, check out the Gallerie Dior and the Perfume Museum (free).

Visiting Versailles is also a must do.