An underground village in the Somme in Picardy; ancient monasteries closed for centuries; a private house with incomparable ancient Roman mosaics from the 4th century; the industrial building of Halles des Boulegrins in Reims, built at the beginning of the 20th century with a revolutionary technique in concrete. All these buildings and a whole host more will open their doors for 2 days only to the pubic. On the weekend of September 15th and 16th, you get the chance to go behind those normally closed doors so take advantage of the chance.
Try to get to the local tourist office in advance. They can let you know what is exceptionally open in the area. Most of the state-run buildings are free, but there may be a charge for some and also for some of the private buildings.