The Shadow Directory was a secret French organisation. It was created by the French Directory to deal with unnatural occurrences. The United States had an equivalent group called the Special Congress.
In 1799, agents Tourette, Marielle Duquesne and Raphael were sent by the Directory to investigate what was happening in Woodwicke. After the Carnival Queen had been banished again from the rational universe, they put out an order to "retire" Duquesne since she may have been tainted by the extraterrestrial influence that had been there. (PROSE: Christmas on a Rational Planet)
It still existed a century later, where the Seventh Doctor again encountered the group in Paris. (PROSE: The Death of Art)