The main challenge seems to be modelling the spheres ... I've got absolutely no idea, if any usual in trade item would match the prototype ...

Yes ... lots of modeling potential there ... and, somehow, I like the idea of rendering the scene in black and white ...
Spheres? Easy ... go to the toy shop, the sporting goods shop, collect various cheap balls of the desired size ...
For the rings around the spheres, check the web for a "circle cutter" ... there are MANY different styles, ranging from very cheap to rather expensive. A fairly cheap one will do the job if you cut the rings from card stock ...

So, the spheres and rings should be easy ... and then you can go crazy with all the little details from there!

BTW, I struggled to understand that "simple" children's story when I studied French ... now that I have the idea, I
might be able to follow along in German. Looks like a really nice visualization of the story in that show ...
Have fun!
Dallas