The Cluny Museum, located in the 5th arrondissement, is one of my favorite museums in Paris. It was formerly the town house (hôtel) of the abbots of Cluny, started in 1334. The structure was rebuilt by Jacques d'Amboise, abbot of Cluny from 1485-1510. The building combines Gothic and Renaissance elements. In 1843 it was made into a public museum to contain relics of France's Gothic past. The museum houses the famous La Dame à la Licorne (The Lady and the Unicorn) tapestries as well as beautiful stained glass windows, illuminated manuscripts and other artifacts from the Middle Ages. Be sure to check out the Gallo-Roman baths dating from the third century which were recently excavated as well as the fabulous vaulted gothic chapel. Take some time to explore this interesting small museum.
This very old building (among the oldest in Paris) was a great structure in its day. They have a collection of artifacts dating back as far as 12th century. The one photographed here is not that old but it was my favorite.