In the French royal family, Madame had a special usage. Rather than refer to royals as "Princess X," as is done in the British system, a variety of titles were used. The king's brother's wife was usually known simply as Madame. No Royal Highness, no princess. The king's eldest daughter was Madame Royale or Madame, if no one else was using that title. All other daughters of the king were known as Madame X", for example, Madame Marie, Madame Adélaïde, Madame Catherine.
In time, the daughters of the Dauphin were also allowed to use this title. The daughters of the king and of the Dauphin were together called the "filles de France" (daughters of France). Male and female princes together comprised the category enfants de France.