When I visited Versailles, one of the features that was pointed out in Marie Antoinette's rooms was a hidden door that she used to escape the palace when it was overrun by the Paris mob. The passage connected the Queen's apartments to the King's Apartments.
Certainly there is. In fact Bran Castle where Dracula is based is famous for having many secret tunnels and are even discovering more .
The Castle of Montbazon (10th century, one of the oldest in France) had a secret passage to the church of the city, 100m from the walls. It may have had others, but they can't be explored anymore.