Chief Warrant Officer Parquet is a native of LaPlace. He is the son of the late Randell Parquet Sr. and Emily Parquet and brother of Randell Parquet, Kimberly Jackson and Valerie Parquet. He began his naval career by enlisting in August 1981. After graduating from Recruit Training Command in San Diego in October 1981, he attended Seaman Apprentice Training and was detailed as an undesignated Seaman. He was assigned to the USS San Bernardino (LST-1189), USS Ajax (AR-6), USS Bagley (FF-1069), Recruit Training Command San Diego, and Amphibious Construction Battalion – One where he attained the rank of Chief Petty Officer. Three years later he was assigned to Shore Intermediate Maintenance Activity (SIMA, San Diego), USS Harpers Ferry (LSD-49) earning his commission as a Chief Warrant Officer in May 2000.