What does mon petit trianon mean?

It means my little trianon.

Le Trianon is a toy hamlet built in the park of the Versailles palace, where the queen Marie-Antoinette pretended to play the shepherdess. There were two of these decorative hamlets, a small one (le Grand Trianon) and a tiny one, (le Petit Trianon) which is essentially a small rococo castle, in the park of the palace. The French middle-class who were able to build some property often refered pleasantly to their place as their 'petit Trianon', as if it was something lavish and fit for the queen herself.