Could be a "livery button", not 100% sure though. For info on the manufacturer via the back mark, A.M & Cie. ("A. M. & Co.") was a major French button manufacturer founded in Paris in 1853 and remained in existence until its defunct sometime in the 1960s. The company name as such was engraved on many french buttons around and during WW1.
As HuntH mentioned, the company was founded in 1853. The founder was Deshavess Masse et Cie.
The company was then taken over by Marre A. and Anglade. Alexandre Masse was a French industrialist and inventor. He was the author of an invention of modest appearance, but which was an innovation of world importance: the garment button with four holes for better fixation.
Source: https://translate.google.com/transl...wiki/Alexandre_Mass%C3%A9&prev=search&pto=aue
Don....
Yep, but note the spelling is ‘Deshayess’ (with a ‘y’) not ‘Deshavess’ (with a ‘v’).
The emblem is a coronet, not a crown, so it’s for nobility not monarchy. On French buttons, these are often incorrectly referred to a ‘Marquis’ or ‘Comte’ emblems but this one is derived from the ‘Adelskrone’ used by Princes in the days of the Holy Roman Empire and then by untitled nobility in later successor states.
It might be livery-related, but has no particular family or authority connection. More likely it’s a pretentious generic ‘pseudo-livery’ fashion button.