Paris with two kids ages 9 & 11

Just a few….Go up in the Eiffel Tower, climb up the steps in the Arc de Triumph, there are carousels all over the city, my grandkids loved the sweet crepes stands and the gelato cones formed like petals. Take the train to Versailles where there’s biking, rowboats, fountains and Marie Antionette’s fairy tale like farm. Have their portraits done at the art market in Montmartre.

Chateau Vincennes is right on the Paris metro end of line 1 and is a very classic fortified castle. If the kids have not visited chateaux and fortifications elsewhere then this is easily accessible and impressive. When we were there last year there were a couple of swordsment leaping about and fencing on the stairs of the tower -- I doubt that is predictable but it was fun. I got a really good model castle of high quality cardboard pieces in the gift shop that my 7 year old grandson loved putting together.

Any itinerary and suggestions will depend on your "9 and 11 year old"'s interests and activity level. Paris is easy to get around with public transport. Easy to navigate and learn how to go by Metro. When we traveled to Paris with my teenage daughter the Musee Rodin was a highlight and doable for her interest level. The Louvre was enormous to do in a day, obviously. The Jardin du Luxembourg was also a nice day near St. Germaine to spend time there. They can sail a vintage toy boat or ride the carousel.
When my daughter visited Paris as a teenager I did a scavenger hunt for the Louvre and the Rodin museum. Not too hard to find on line, but I made it myself with the major works of art. The museum website tells which room the artwork can be found(to give you hints) and a little history of the artist. We were able to hit the highlights without exhaustion. We also did a form of scavenger hunt like "challenge" to find the best crepe, best chocolate chaud. That might appeal if they have foodie/culinary interests. Ask them and get creative using their suggestions! That way they are more engaged in the trip instead of bored and feel like they are just being schlept around.
P. message me if you'd like more details on the scavenger hunts.

We did this in 2019 when our kids were 10 and 12. Here are a few thoughts.

1) Luxembourg gardens is a good spot to let them relax and run around.
2) The Cluney Museum is a small museum that our kids enjoyed.
3) Do a day trip to Versailles but make sure you rope drop it. Don't wait until noon.

You should also let your kids explore the neighborhood you're staying in. They'll find a cafe or bakery or chocolate shop that they'll love. My kids found a board game store in the Latin Quarter that they swung into several times. Don't over-plan it, give them a lot of time to walk and just see the city.

You should try a boat trip on the Seine (we take Bateau Mouches). And consider doing one at night, since all the monuments are lit up. The gardens outside are lovely, and you can rent bikes. If kids are into wars, the War Museum and the Bonaparte tomb could be fun. If they are ghoulish, the catacombs might appeal to them. I also second crepes, because you can almost build your own and they are relatively inexpensive. Be aware that there are two kinds: galettes, which are dinner crepes, and crepes, which are dessert. There are a lot of crepe restaurants near Gare Montparnasse.