Thanks to my sister, I now know what this is:
It's called a Hedge Apple or a Bois d'arc.
I don't think they're edible but it seems they are very craftable and their wood is highly desired for making bows for stringed instruments. My favorite use for them was as a tennis ball replacement for Layla's game of fetch as we walked by the lake. Oh, and it has been said that they keep spiders away.
I guess I should consider myself lucky for having come across one of these here in Switzerland. Unfortunately by the time I found out what they were the fruits had fallen off the tree and been swept away by the super efficient Villeneuve municipal landscape crew. Oh well, I'm not very crafty anyway.
Now we can all (yes, all three of you my dear readers) rest easy knowing what we've found.