I did a trip to Paris with my 11 year old daughter a couple years ago and got lots of good ideas from this board.
For shopping, she actually had a great time at the Monoprix in Les Halles. I would say it is a little like a French Target, with groceries on one level and clothes, pharmacy, and other items on the lower level. Prices were very reasonable, but they carried French brands you can’t get here!
We also went perfume shopping at Goutal. The sales lady helped us try a bunch of scents and gave her a bunch of samples when we bought a small bottle of each de toilette—a fun French shopping experience.
https://maps.app.goo.gl/rzHkKpYcdneuPkWk7?g_st=ic
For other activities, she loved the bike tour of Versailles with Fat Tire Tours (which includes shopping for a picnic lunch at the local outdoor market in Versailles). I think it would be great for your son as well.
And a terrific recommendation I got from this board was a cooking class near the Eiffel Tower. It’s Oliver’s Table on AirBnB experiences. We did the crepes class and it was one of the best things we did (would be great for the whole family). Delicious food and a wonderful instructor/host:
https://abnb.me/WxhLTfeQ3Gb