There were so many button manufacturers in Paris in the 18th-19th centuries, that “Paris Back” is an entire category among button collectors.
I have loads of them.
The back marks are as interesting as the front designs.
Here are a few relevant internet resources, googled up for you
https://boutonsweb.fr/collectionboutons/Marques.html
https://www.rodblunt.com/button-backmarks
https://fr.wikipedia.org/wiki/Alphonse_Desaide
Desaide was an engraver . in this listing
https://www.catawiki.com/fr/l/9026707-france-medaille-republique-francaise-a-desaide-argent
it says “In 1890, he was mentioned as a “heraldic engraver” still at the Quai des Orfèvres, and editor of a book by Louis de La Roque, Heraldic Devises, translated and explained.”
Jamais l'or n'a perdu la plus petite occasion de se montrer stupide. -Balzac