Sponsored Topics. Fairfield is a town in Teton County, Montana, United States. The population was 659 at the 2000 census. Fairfield is located at 47°36′55″N 111°58′51″W / 47.61528°N 111.98083°W / 47.61528; -111.98083 (47.615250, -111.980859). According to the United States Census Bureau, the town has a total area of 0.3 square miles (0.8 km²), all of it land.