Any ideas for cool things to do with a one year old and a five year old?

Off the top off my head I would recommend:

https://www.cite-sciences.fr/en/explore/permanent-exhibitions/cite-des-enfants/cite-des-enfants-2-6

https://aquariumdeparis.com/en/

https://www.parczoologiquedeparis.fr/en

https://www.jardindacclimatation.fr/en

https://www.lemondedenoe.fr/

https://philharmoniedeparis.fr/en/philharmoniedesenfants

https://maps.app.goo.gl/dk5ReQsW5v9YHHF6A

I need to go to bed, so I'll need to come back later and elaborate and drop some more tips but those options are a good starting point.

I can second the first one (Parc de la Vilette). I've been there both as a kid (although not as young as yours) and as an adult and I always liked it there. Lots of things to do and to explore. The one year old will not be able to participate in much, but if your five your old likes science museums he or she will love it.

Jardin du Luxembourg is a free garden with a lot of statues and chairs for everybody to sit on. There is a big pool in the middle, which has rentable RC boats.

Bring an empty bottle / flask, as it’ll get quite hot (>30°) and the kids and you will need to keep hydrated.

Go to museeums, they are pletora. There plenty of cool stuff/experiment for kids on the musée d'histoire naturelle but there is plenty other on every theme in Paris.

You should crosspost this on !forumlibre@jlai.lu to reach many french at one time.

Thank you all for the recommendations, we’ll give (some of) them a try