Finally found one: https://meaningcrafters.com/produit/powerbank-alex/
I don't speak French but placing the order was quite straightforward. Shipping costs were a bit high, but totally worth it. ~~Highly recommended!~~
Edit: Probably too good to be true, see discussion below...
I can't say I like their website, at least not their product page. There's a paragraph of mostly meaningless marketing-blabla, and even the "Paramètres Techniques" page does not list the most important aspect of a powerbank, the capacity. You have to go to "Téléchargement" and download a single-page PDF leaflet to find that out.
And then it's just 10000 mAh. My 15 year old Anker powerbank has 16000 at a similar form factor. Talk about disappointing.
At least they use only very simple french words, I had no problem at all with my rusty old highschool french from ages ago…
* Edit: I just noticed, the products list "Batterie Externe" lists the capacities of the various products front and center, very visible.