The kitchens at Valençay are famous because the château's 19th century owner, Talleyrand (Napoleon Bonaparte's foreign minister) had in his employ one of the great figures in the history of French gastronomy and cooking. His name was Marie-Antoine (a.k.a. Antonin) Carême (1784-1833). It has been said that Carême refined and developed techniques and ideas brought to France by Catherine de Médicis, the Italian queen of France who lived for a while at the Château de Chenonceau, where you can also visit the kitchens. The kitchens at Valençay are in the basement of the west wing of the château.
There's an interesting article here in the regional Nouvelle République newspaper about Antonin Carême's life and influence. While the Wikipédia article about the Château de Valençay says sort of snootily that that rien ne prouve qu'il [Carême] a séjourné au Château de Valençay, he worked as a cook for Talleyrand for 12 years. Somewhere else I read that he was the first cook to be called chef in France. He was known as le roi des chefs et le chef des rois. Maybe he just stayed in Paris and had staff that took care of the cooking at Valençay following his instructions. It has been written that cooking on wood fires and inhaling a lot of toxic smoke for many years might be reasons why he died prematurely at age 48.