Real Dictionary

madame in American English
a married woman: French title equivalent to Mrs.: used in English as a title of respect for a distinguished woman or generally for any foreign married woman
noun: a French title of respect equivalent to “Mrs.”, used alone or prefixed to a woman's married name or title

madame in British English
noun: 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