formal term of address to a lady, 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. It is more formal or affected than madam. OED recommends madam as an English title, madame in reference to foreign women.
early 14c., "a quarrel, dispute, disagreement" (now archaic), from Old French debat, from debatre(see debate (v.)). Sense of "contention by argument" is from late 14c., that of "a formal dispute, a debating contest, interchange of arguments in a somewhat formal manner" is perhaps from early 15c.