Where is this in Paris?

Whether you find that same spot or not, I think you'll be able to capture that feeling almost anywhere in Paris. It sounds like a lot of places.

There's not a lot of non-luxury shopping along the Seine. I remember that there is a plant shop and a pet shop when walking away from the Place du Châtelet, towards Pont Neuf. But Paris is subject to gentrification, like any other city.

Can you remember WHICH side of the Seine had the stores? The shopping on the shore opposite Notre Dame is picturesque, but I'm not sure it's as "genuine" as you remember. There are plenty of authentic "neighborhoods" in Paris, even if they don't have a view of the river.

Are you perhaps thinking of the licensed sidewalk vendors, like these? You can browse for yourself using GoogleMaps in the street view mode.

I've done that walk. Your memory is correct - it's right along the Seine. It's the pet shops that jogged my memory. Here's a link to a little story about the area. http://www.dailymail.co.uk/travel/article-1284705/Paris-How-children-entertained-French-capital.html

Thé plant stores are there but there have been problems with the pet shops - most of the animals came from illégal puppy and kitty mills outside of France. I believe only one pet store is still there. The others have been closed or turned into shops selling trendy furniture.
If you cross over to the Left Bank, on Sundays, you can go see the bird and flower market.

Could it have been on Ile St-Louis?

Marché aux Fleurs is on the Ile de la Cité. The merchants chexbres is describing are on the right bank between Chatelet and the Louvre but closer to Chatelet, up on the Quai.

I believe you are thinking of Marche aux Fleurs et aux Oiseaux on the Île de la Cité. "Located on Place Louis Lépine between the Notre-Dame Cathedral and Sainte-Chapelle chapel, the flower market has attracted avid gardeners and curious passersby since 1830. Both covered and open-air, the market is mainly formed by pavilions from the 1900s. Their selection is huge: seasonal flowers, exotic flowers, orchids, plants, shrubs ... a unique and endearing place for a walk."

There are many flower shops and bird shops there. Or you might have come across a market set up for the day.

It would appear that Valerie has identified the place. Merci!