) Eastern ( UTC-4 ) ZIP code 02540 Area code(s) 508 / 774 FIPS code 25-23105 GNIS feature ID 0618253 Website: http://www.town.falmouth.ma.us/ Falmouth is a town in Barnstable County , Massachusetts , United States ; Barnstable County is coextensive with Cape Cod . The population was 32,660 at the 2000 census.