"brownish-purple," literally "flea-color," 1787, from French puce "flea-color; flea," from Latin pucilem (nominative pulex) "flea," from PIE *plou- "flea" (source also of Sanskrit plusih, Greek psylla, Old Church Slavonic blucha, Lithuanian blusa, Armenian lu "flea").
[T]he couleur de Puce, or flea colour, and the couleur de Noix, or nut colour, are the reigning winter taste. [Westminster Magazine, January 1777]
Perhaps so called as the color of the scab or stain that marked a flea-bite; flea-bitten was a color word in English to describe whiter or gray spotted over with dark-reddish spots (by 1620s, often of the skins of horses, dogs, etc.). That it could be generally recognized as a color seems a testimony to our ancestors' intimacy with vermin.
OED sees no connection between this word and obsolete puke (16c.-18c.; hence Shakespeare's puke-stocking) as the name of a dark color of now-uncertain shade (Century Dictionary says perhaps reddish-brown, OED says bluish-black or inky; others suggest grey).