Cotillon / Cotillion / Contredanse Française
referring to a dance in our collection:
The dance is a contredanse from de la Cuisse, published in 1762. It was not called a cotillion in France. Once de la Cuisse had published his collection, the contredanses became popular in England and were simplified (fewer figures but the same idea of a main chorus with changing verses) and called them by the old name they were known as in France, cotillon, anglicised as cotillion. I think this must have been because the term country dance was already in use, so contre danse just didn't fly. In America, they were sometimes called French country dances or English country dances, but gradually the term cotillion took over.
Roughly outlined, the dance type was inspired by English country dances, that were first introduced at Louis XIV court in the 1680s. My understanding of what happened is this: the court didn't like the idea of progression (the King doesn't stand second to anyone), so took the figures and used them in a non-progressive formation. There was a verse-chorus dance (for 2 couples only) and a particular tune called cotillon floating around in 1690-1710 (the tune made it into the Beggar's Opera). Somehow, the English figures and the verse-chorus dance merged into a complex square dance with a refrain that became known as contredanse. It was the rage although sometimes not very successful, at the Opera Balls in the 1720s -50s (see Semmens, "Les bals publiques"). I gather it was de la Cuisse who figured out a way to write the figures down first, because we have records of contredanses being danced, but no figures until his book in 1762.