a married Frenchwoman: usually used as a title equivalent to Mrs, and sometimes extended to older unmarried women to show respect and to women of other nationalities
Word Origin
C17: from French. See madam
Word Origin and History for madame
1590s, see madam, which is an earlier borrowing of the same French phrase. Originally a title of respect for a woman of rank, now given to any married woman. OED recommends madam as an English title, madame in reference to foreign women.