The posts on both the BuyInEU communities seem pretty serious lately, but after reading latest Derek Guy's (dieworkwear.com) "Excited to Wear This Spring" post, I found Filt - the French net shopping bag manufacturer that makes their bags (and other stuff) in France
Also here's a tag from a random Vinted listing:
The "organic" part though doesn't seem to be mentioned in the product listings on the website? hm
EDIT: Just received a package with one ecru (natural colored) bag and one black-and white one. The ecru one says organic cotton while the colored one uses regular cotton. So if you want organic get the ecru version
Bio can mean organic, right? At least it's used in Germany and the EU label for organic stuff also reads "Bio".
same in France "bio" means organic
Probably this part for organic: The Élysée X Filt1860 shopping net is 100% cotton.