Le Valois is a traditional French brasserie on the Place du Marché Notre-Dame, with tables on the square itself when the weather allows. It is unpretentious and reliable — steak frites, moules marinières, duck confit, a decent wine list led by glass carafes of house Burgundy.
The location makes it a natural choice for lunch after a morning in the palace: it is 15 minutes' walk away, the food arrives quickly, and you can sit outside and watch the market square. The clientele is a mix of locals and well-organised tourists who have figured out that eating near the market is better than eating near the palace.
Service is businesslike rather than warm, in the Parisian brasserie tradition. Prices are honest for the area. Go early (before 12.30) or accept a wait.