The Vienna, or La Viennoise, is a late nineteenth century schottische variant which originated in America and traveled to France with the inimitable George Washington Lopp, though it's not clear to me whether it had much (or any) popularity there or, for that matter, in America.

My first American source for the dance was, unsurprisingly, M. B. Gilbert's Round Dancing (Portland, Maine, 1890), which collected a wide assortment of the couple dances of the 1870s and 1880s. Gilbert and Lopp (in La Danse, 1903) agreed on how the Vienna was danced. Going with Gilbert's description, giving the gentleman's steps (lady dances opposite):

The Vienna (four measures of 4/4 schottische music)
(joining right hands with partner, facing the opposite direction)1b Slide-cut-leap-hop forward, starting left, raising right to fourth on the hop
1b Repeat, starting on right foot

1b Slide left to side (1), close right to left (2), leap back onto left (&), slide right to side (3), close left to right (4)
1b Repeat, starting on right foot, leaping forward

Lopp mostly agreed, though he had the final repeat also leaping backward, which I believe to have been an editing error, since his instructions are otherwise almost word-for-word from Gilbert, translated into French.

There are...some problems with this...[and I talk about them behind the cut]