Echo (see Collins dictionary) derives from the Greek word ἠχώ, and means a softer, delayed repetition of the same sound, in the physical sense caused by reflection. So it does not relate to a dance. I learned, that in the French Ouverture the Echo movement is no softer repetition of an earlier movement, but alternates between stronger and softer passages (why short of a fully dynamic piano a two-manual harpsichord is required).
Bach was apparently fond of that effect, since the Christmas oratorio (wikipedia) has an extra echo soprano repeating, what the first soprano sung before.
Addressing a comment to the question: The word écossaise, being the French translation of Scottish is unrelated to echo.