The Phrygian Cap* was originally a symbol worn by Paris (son of Prima, from Phrygia) that would be taken up in late Roman iconography, well before it became a symbol of the Parisian sans-culottes. Revolutionary aesthetics were particularly inspired by classical culture and, therefore, by the Greco-Roman world. The pileus was a soft, conical cap given by Roman masters to their slaves once they were freed. The cap was adopted by the sans-culottes in 1792.
* For two years I made someone at school believe that the Phrygian Cap was a form of birth control. No real relevance here. I'm just proud.