Fulton County is a county located in the U.S. state of Indiana. As of 2020, the population was 20,480. The county seat is Rochester. The first non-Native Americans to ever set foot in what is now Fulton County, Indiana, were French traders. Few of them remained permanently as year-round residents of the area and by the 1830s there was no French populati…Fulton County is a county located in the U.S. state of Indiana. As of 2020, the population was 20,480. The county seat is Rochester. The first non-Native Americans to ever set foot in what is now Fulton County, Indiana, were French traders. Few of them remained permanently as year-round residents of the area and by the 1830s there was no French population in what is now Fulton County.