1816, "patterned wooden flooring," from French parquet "wooden flooring; enclosed portion of a park," from Old French parchet (14c.) "small compartment, enclosed space; part of a park or theater," diminutive of parc (see park (n.)).
Meaning "part of a theater auditorium at the front of the ground floor" is recorded by 1754 in a French context. The noun use in English has been influenced by the verb meaning "provide with a floor of parquet work" (attested from 1640s, from French parqueter. Related: Parquetry "inlaid flooring in which a pattern is formed by different types of wood" (1842).