Re: A.M & Cie Button
The button-backmarks book says A.M. & Cie is an unidentified French firm, dating from the World War One era. Cie is the French word for a business company.
For anybody who doesn't already know... "the button backmarks book" is "American Military Button Makers and Dealers; Their Backmarks & Dates" - by William F. McGuinn and Bruce S. Bazelon. (It also includes many British and French button-makers & dealers.) It covers backmarks from the late-1700s through the late 20th-century. Costs about $25, and I guarantee you'll never regret buying it.