madam vs grande dame

madam and grande dame both are nouns.

Word	Noun	Adjective	Verb	Adverb
madam	Yes	No	No	No
grande dame	Yes	No	No	No

As nouns, grande dame is a hyponym of madam; that is, grande dame is a word with a more specific, narrower meaning than madam:

madam: a woman of refinement
grande dame: a middle-aged or elderly woman who is stylish and highly respected

madam (noun)	grande dame (noun)
a woman of refinement	a middle-aged or elderly woman who is stylish and highly respected
a woman who runs a house of prostitution