David Price authored a history of the cancan. It appears that the raised skirts were a later addition, specifically connected with the fashion for frilly underwear in the 1890s.
The cancan developed from the galop, a popular dance in the public dancing gardens and dance-halls of Paris in the early part of the nineteenth century. When it first appeared in 1830, the cancan was really an exaggerated form of the galop, with high kicks and other gestures with arms and legs, mostly initially performed by men, and later also by their female partners. It was viewed as shocking by “respectable” people because it implied a lack of self-control and involved more bodily contact between participants than was thought acceptable.
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The element of skirt manipulation, essential to the cancan today, only really became part of the cancan in the 1890s, with the appearance of the elaborate erotic underwear characteristic of the turn of the century.