In Paris, skip going to the top of the Eiffel Tower. Tickets are almost impossible to get (hearing lots of horror stories), plus, the pictures you take, don't you wan the tower in them? Last time we were there, we did a private boat tour on the Seine. It involved copious amounts of Champagne, a cute captain, and a lot of fun. I highly recommend doing this vs. the big tourist boats. This is who we used (https://www.airbnb.com/experiences/194776?adults=1&checkin=&checkout=&children=0&infants=0&pets=0¤tTab=all_tab&federatedSearchId=&searchId=&source=wishlist)
While I think the Louvre and the Musee d'Orsay are musts, they eat up a lot of time. Buying tickets in advance helps. Also, try and plot your route through to hit the highlights. Pro tip, the Mona Lisa is really small, and there are much better paintings in the main gallery leading to this small one where she sits. I love Delacroix's Liberty Leading the People, the Coronation of Josephine by Jacques Louis-David, and of course both the Venus de Milo and the Nike of Samothrace. If impressionists are more your bag, the Musee d'Orsay is outstanding, but same advice. Pick what you want to see and plan your route. You can do both in one day if you plan well. Pick one for the AM, one for the afternoon, and do lunch at Les Deux Colombes (which is a bit of a long walk, but the view!).
On shopping, Goyard no longer does appointments, so you have to queue. However, you can still get a deal there and in LV compared to the US. Not many other deals to be had (Hermes and Chanel do a good job of managing FX and arbitrage opportunities with their pricing). If you are more interested in vintage finds, let me know. I have been compiling a list of places.
On restaurants, I loved MoSuke last time I was there. Mory Sacko has opened a new place as well (Lafayette's). Also, many people raved about Les Parisiens, which is also on my list for next trip.
Those are my highlights in 5 minutes or less.