Madame is the way to address a French woman, as in Madame Curie. It’s officially for married women, like Mrs. in English, but it’s often used for any exotic woman, married and French or not.
The title madame is sometimes used interchangeably with madam or ma'am, although usually the first one is intended for French-speakers. In Gustave Flaubert's novel Madame Bovary, the main character, Emma Bovary, is a married woman. Madame was originally used only to refer to or address women of high rank or royalty. In French, madame literally means "my lady."