Gouverneur is a town in St. Lawrence County, New York, United States. As of the 2020 census, the population was 6,551. That was down fro…Gouverneur is a town in St. Lawrence County, New York, United States. As of the 2020 census, the population was 6,551. That was down from 7,085 in 2010. The town is named after statesman and landowner Gouverneur Morris.