Right Bank of the Seine River Promenade

If there's one thing you do in Paris, it should be to stroll along a promenade on a bank of the Seine River! You walk under the most beautiful sandstone bridges, and see architecture that will make your heart soar! The color of the water is the loveliest jade green. Along the way, you will see runners, couples embracing, and people eating baguettes while their legs swing over the edge of the stone walls.

The north side of the river has the Right embankment and the south side of the river has the Left embankment. You can stroll along the river, up high above the river or at river level, and river level is what I am writing about here. The Right embankment was a former road, so the path is asphalt and wide. Some areas of the path are cobblestone, but still fairly wide. This leaves plenty of space so that you don't feel crowded out by people like you do on other walks in Paris.
We started our walk at Pont d'Arcole on the Right embankment, and walked west. Above us soared glorious buildings like the Hotel de Ville (city hall) and Louvre, while across the river we saw adorable medieval architecture of the Conciergerie. My eyes were transfixed on it. In the middle of the river, we saw the two islands, with willow trees on their points, where people sit and relax.
We walked under Pont Notre Dame, a very old bridge, with its heads of Dionysus on each arch. Pont au Change has letter Ns on each arch. Pont Neuf, my favorite, is of the sweetest rounded shapes and sandstone color. It is the first place I went in Paris when I arrived as a 19 year old studying abroad. Then Pont des Arts, the metal bridge with romantic lampposts spans the river, and willow trees frame the view. 
There are little playground areas with ladders, tree trunks, and climbing spots for kids along the way, plus small cafes where you can sit in the sun. 
You can keep walking west or east for miles. I would like to continue this walk all the way to glorious Pont Alex III one day.
And you can walk the left embankment of the Seine River too. It's wonderful to see how many people are enjoying the pedestrian-only nature of the roads here.
Voie Georges Pompidou is the name of this former street, on google maps, that has been transformed into a pedestrian paradise!
The marathon race for the 2024 Olympics took place here, and there were colorful paintings on the path.

Directions

You can start your walk anywhere along the river in the center of Paris. Just walk down a stone staircase or a street ramp, when you see one, and you will reach the river level. There is a ramp leading down, at Pont d'Arcole, across the street from Hotel de Ville, if you want to start there. 
Voie Georges Pompidou is the name on google maps of this former-street-now-promenade that runs along the Seine's right embankment.

Click on map for interactive view