Soaking feet can remove athlete’s foot, but there is no research indicating that soaking feet in river water can remove athlete’s foot.
To remove athlete’s foot, soak your feet in hot water instead of cold water. Soaking your feet can accelerate blood circulation and allow the cells on your feet to relax, thereby removing athlete’s foot.
Of course, although soaking feet in river water may not help remove athlete’s foot, I think soaking feet in seawater is helpful because seawater has a high salt content.