First Time In Paris! Traveling With Seven Year Old

Finding rooms for 3 is tricky and it is late to be looking. I'd run a screen using your dates and for 3 to a room on booking or similar search engine and identify things that are available and then get feedback. Screen for 3 people and AC. You must book for a triple room -- you will not be allowed to put 3 people in a double room even if you are willing to 'make it work.' This is very strict generally in Paris. An apartment hotel with one bedroom might be nice because you could put the kid to bed and still be up in the living area/ fold out bed area.

Our 8 year old grandson loved Chateau Vincennes which is like a kid's idea of a castle and easily reached on the metro 1.

He also really did love the Eiffel tower -- get tickets to the top when you can. We had a day when it was pouring rain but the good part was that we had no lines -- we just walked on to the first elevator and when we got to the second floor where the elevator usually take an hour or more in line -- we got the next elevator to the top -- so the kid was happy in the rain and brags about how cool it was that he didn't have to be in a crowd.

Arrange to visit the Luxembourg gardens. I don't know the times in July -- when we were there the small boats were available weekend afternoons and Wednesday afternoon. We were there on a Sunday and had a wait for a boat -- but sailing a model boat on the fountain pool was a highlight of his trip. And it is a peak photo op.

If you go to the Louis Vuitton Fondation museum -- and it is always an amazing exhibit -- after you see the art, you can walk for free into the Jardin Acclimatation which is an ancient amusement park ideal for a 7 year old. You can buy ride tickets from machines, but the park entrance is free from the museum. We were there for a Calder exhibit in April and our kid was fascinated with Calder's circus and the mobiles --

janettravels gives you excellent advice, especially about getting a triple room. Trying to accommodate three in a double room could leave you without lodging. It is quite late to be searching for a room for July. I would go to Booking.com and enter all your parameters (A/.C, triple, price range, etc.) I find Booking.com to be a reliable source for lodging, whether you book through them or the hotel itself. Since you mention being up for luxury-type accomodations, you may have better luck finding a room.

We took our kids to Paris for the first time when they were 8 and 10. They loved the Eiffel Tower, the boat ride on the Seine (Vedettes de Pont Neuf, top deck), the Invalides (Army museum) for the suits of armor, etc., the statues in the Rodin Museum garden (so big!), sailing boats in the Luxembourg Gardens, eating crepes purchased from the sellers on the boulevards, looking through the knickknacks, posters, etc. at the bouquinistes along the left bank of the Seine, and were impressed with Notre Dame (their first big cathedral experience). They also got a kick out of wandering through a French grocery, comparing the snacks, etc. to those in the US. It took a day or so for them to lose their shyness about saying French words (merci, s'il vous plait, bonjour, etc.), but we could see a little bit of pride in themselves when they did, and they grew more comfortable as the days passed. The metro ride was new for them (we're from Southern Calif.) and was a kick for them also.
Amusez-vous bien!

What might be fun is going to a McDonalds's to compare with home. It's called McDo. Since you only have four nights, that is three full days plus part of a day (on arrival or departure) you will have to narrow down your places to visit. We didn't try to have our kids see three big things in a day, but sometimes that did work out. I suggest a kind of early start by going to a bakery for breakfast (croissant and hot chocolate, perhaps). Then to the first sight you have chosen (get the earliest reservation you can to minimize crowds and waiting). Stroll a bit if you finish before lunchtime. Then a relaxing lunch at a sidewalk cafe to people watch and rest your feet. In the afternoon go to your second planned sight. Depending on whereabouts you are, you could add something else before a (possible) rest at your hotel before dinner. (e.g. Eiffel Tower in the morning. If you don't go up, then follow your gander at it with a walk to the army museum. Spend an hour or so there, then lunch . If you go up the tower, have lunch after descending then go to the army museum. From the army museum you could walk to the Rodin museum and see the garden sculptures. Have another sit-down with a drink....coffee, aperitif, soda, etc.) A lot depends on how long you spend at a place. Be flexible. Many places need reservations, and many don't. If the grandson gets tired, relax at one of Paris' lovely parks or head to your hotel for that before-dinner rest.
Oh yes! Picking out a yummy breakfast at a bakery was a treat for our kids. Try a different one each day. There are tons of them to choose from. Let the grandson pick out a treat from an ice cream store or a patisserie for an afternoon snack.

Another thought. Don't underestimate your grandson's possible interest in some art museums. I recall that there was a WOW moment for my daughter when she first saw the altar triptych at the Hospice de Beaune. It was like a switch was turned on in her brain. It didn't make her a big art museum fan right away, but it did change the way she took in the art-centric places we did visit. When we subsequently made it to Paris she enjoyed our "taste" of the Louvre. (We only spent about an hour there back then. This was 1988 when no reservations were needed and we could go back easily without feeling we needed to see it all in one go.) You may not have time for an art museum in your brief stay in Paris, but who knows? Do check out a guidebook or two for suggestions. I know we missed many things back then, and we had a week with the kids, and both of us adults had been to Paris before.

Bustronome is fun, and the food is better than you might expect. In late July, you should catch the sunset on the dinner outing.