After 40 years as a French teacher, and leading 20 student groups to France, I can tell you with certainty that many people see the Eiffel Tower as the symbol of Paris. I have seen students cry when they see it in person, and my granddaughter took 150 pictures of it on a recent visit.
At the risk of alienating all the Eiffel Tower lovers, I have to admit it is my least favorite place in France and possibly the world. Without going into my reasons and being negative about a well-loved landmark I would like to suggest a few other spots in Paris you might enjoy.
If you want to see the Eiffel Tower but you don’t need to go up in it, take one of the boat tours on the Seine. There are a variety to choose from including dinner cruises. We went on the Bateaux Mouches tour and had fun. I would recommend buying tickets in advance no matter what you do. We had the best results at the official tourist office in Paris at https://parisjetaime.com/eng/tickets?gclid=Cj0KCQjwpompBhDZARIsAFD_Fp-JZEFhLIFnGfwNLkUallT9q5kIxrcCFb06TEuz_tPG1S02Z4VYHTkaAk43EALw_wcB
We have also used Viator at https://www.viator.com/Paris-tourism but we had a few issues with them.
Try a cooking class. We went to Galleries Lafayette for a one-hour class on making Macarons. It was amazing, and although many of the cooking classes are expensive this one was $60.
The parks in Paris are so much more than green spaces. Luxembourg Gardens is a peaceful oasis in the city, but it also has a spot to picnic, two cafés, pony rides, a playground, a carrousel, a lake to sail toy boats, a beehive, a vineyard, pétanque and tennis courts, and plenty of history and art. We visited one on this trip called Le Jardin des Plantes. You enter through a tiny door thinking this must be a small park, but it is massive. There was a zoo and many exhibitions.
There are canal rides over near the Bastille.
Go to Forum Les Halles if you want a French mall experience.
If you are standing in front of Notre Dame go to the street behind you and turn the corner to your left. There is a series of plant and gift stores that are fun to walk through.
Although you can take a taxi, a bus, or the metro to get around, consider walking and you will find gems along the way.