I do not speak French, so I did not intervene earlier, but I am trained as a classical philologist (i.e. Latin and Greek), so this statement gave me pause, namely in that it sounds like you don't know what the word noun means.
Traditionally there are 8 parts of speech: noun, verb, pronoun, adjective, adverb, preposition, conjunction, and interjection.
What would "madame" be if not a noun? At most you can call it an agglutination of a noun and a (possessive) adjective, but functionally it would still be used as a noun.
Even if you would use an expanded functional classification of parts of speech, what would "madame" be if not a noun?
Like I said this debate has been during too long for what it's worth but indeed I was wrong and I explained myself poorly. I meant it can't be used as a common noun (I don't know if it's the right word in English) such as "woman". I should have talked about what we call the function of the word (I also don't know if it's called this way in other language) which can be either "apostrophe" (vocative in Latin I think : https://translate.go...n/fr/apostrophe the second definition
), which makes it akin to Milady (I think that would be the best translation in this particular case) in English I believe, or part of the "subject" of a verb, preceding a last name. I don't really see any other use of the word Madame.
I apologize if I've been butchering English grammar 
Anyway it's clearly off topic and not worth spending so much time talking about it, and it seems to annoy some people