Freienbach is a municipality in Höfe District in the canton of Schwyz in Switzerland. Freienbach is first mentioned in 972 as Friginbach. Freieā¦Freienbach is a municipality in Höfe District in the canton of Schwyz in Switzerland. Freienbach is first mentioned in 972 as Friginbach. Freienbach has an area, as of 2006, of 13.8 km². Of this area, 40.7% is used for agricultural purposes, while 23.8% is forested. Of the rest of the land, 31% is settled and the remainder is non-productive.