That word is in use, but not very common nowadays, and the meaning is heavily dependant on the context.

Examples could be:

• polite/honorific, although a bit antiquated: "Was wünschen Madame zu speisen?"
• ironic/derisive, to a girl/teenager: "Wenn ich Madame noch einmal dabei erwische, wie sie an meine Kreditkarte geht, setzt es was!"
  • Mainly used to put said girl's head straight when she thinks she's entitled to something she actually isn't.
• Warning: The english word "madam" is sometimes used to denote a female procuress, too, and this connotation did make some headway into the usage of this word in German.

Anyway, "gnädige Frau" is a more up to date replacement for "Madame", especially for the more positive connotations.

That word is in use, but not very common nowadays, and the meaning is heavily dependant on the context.

Examples could be:

• polite/honorific, although a bit antiquated: "Was wünschen Madame zu speisen?"
• ironic/derisive, to a girl/teenager: "Wenn ich Madame noch einmal dabei erwische, wie sie an meine Kreditkarte geht, setzt es was!"
  • Mainly used to put said girl's head straight when she thinks she's entitled to something she actually isn't.
• Warning: The english word "madam" is sometimes used to denote a procuress, too, and this connotation did make some headway into the usage of this word in German.

Anyway, "gnädige Frau" is a more up to date replacement for "Madame", especially for the more positive connotations.