Sorry for tardiness, OP. I'm in Corfu and having a few tech issues!
You're already ahead of the game in having a hotel with aircon and a pool. We started off in an Airbnb which was so hot that we moved within an hour. We then stayed at the Maison Albar in Pont Neuf which was a fab base. Quiet enough, but within easy striking distance of everything.
Purpose of our trip was language confidence (well, it was for me:DS favoured shopping). We did everything by public transport so he could buy tickets/read signs etc. train from the airport, then metro to Norte Dame (a crying shame to see all the scaffolding).
Travel light! We couldn't check in early so having a couple of backpacks was ideal.
We did the Louvre (a bit disappointing, couldn't get near the Mona Lisa) and also Orsay (better; cooler). Was desperate to do the catacombs, but the thought of them freaked DS out. Was also keen to do lovely cuisine, but ended up having McDonald's (he needed to see the difference, apparently), crepes and jambon fromage from street vendors. Tried a fancy burger restaurant, but the meat was "bleeding" 
There was a lovely bistro next to the hotel for people watching and steak frites though.
The heat was intense. Trocadero fountains next to the Eiffel Tower was amazing. We didn't bother going up it for all the reasons pp mentioned, but you could see it from Trocadero. You could also picnic on the banks and get shot at by water canons.
Other place with great view was Galeries Lafayette. It's a beautiful building, obviously, with very high-end stuff. DS loved hanging his nose over unaffordable wares. The terrace at the top has panoramic views over the city.
From the Louvre, we got a bateau mouche. It was ridiculously hot, so get one with shade if you can. Our didn't. Ended up bailing early and continuing along the bank on foot. The pavement has fountains built in that were very welcome! Lots of little bars built into the bank and vendors selling water. Make sure you have change!
We also hired e-scooters (Lime) outside the hotel through an app, with a view to scooting to the Louvre. That was a disaster. DS was great, but I was hopeless. Managed a couple of streets 
Didn't got to Sacre C as had bag picked before years ago and was mindful of being there alone with DS.
So, for me:
-go to Eiffel, but not up it;
- wouldn't bother with Louvre unless art is the purpose of your trip;
-Orsay/Rodin better:
-Don't expect to turn your DD into adventurous diners unless they already are. Food on the go plus bistros work well;
-If you do the bateaux mouche, get shade and stay hydrated;
-find somewhere (lots of suggestions on this thread plus Galeries Lafayette) with a great view);
-take refuge in hotel pool as an when needed.
Enjoy!