Unlike other unmarried daughters of the nobility who were born demoiselles, the princesses who were the daughters of the kings of France were born with the rank and title of "dame."
A Daughter of France (fille de France) was thus addressed as Madame, followed by her first name or her title if she had one. The treatment was the same with the sole exception that with the eldest, it was not necessary to add the first name, and the simple appellation "Madame" sufficed to designate her.
The sister-in-law of the king was similarly treated. When one existed (this was the case for Louis XIV of France and Louis XVI of France but not for Louis XV, who was the sole surviving sibling), the first of the filles de France was given the title of "Madame Royale."
The appellation of "Mesdames" remained in history because of particular genealogical, political, and strategic circumstances that caused many of the eight daughters that Louis XV had with Marie Leszczynska to remain at the French court, including:
To economise on their maintenance at court, and to prevent the queen (to whom a large, allied brood would give comfort) from having too much influence, the last four of the princesses were raised far from the court, at Poitou in the Fontevraud Abbey from 1738 to 1750, where they passed their formative years before returning to Versailles. Madame Thérèse did not return to Versailles, and Madame Louise came back, but was very strongly influenced by the monastic life, to which she later returned at Carmel de Saint-Denis.