1816, "patterned wooden flooring," from French parquet "wooden flooring; enclosed portion of a park," from Old French parchet (14c.) "small compartment, 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 first recorded 1848. The noun use in English has been influenced by the verb (attested from 1640s, from French parqueter. Related: Parquetry