I wasn't quite sure what the Fremont River Walk was, but I do know that it's in Capitol Reef and that it runs much of the length of Highway 24 in the park. We just happened to spend all of our time along the 24 because the entire remainder of the park was closed due to flooding.
Our trip to Capitol Reef lasted two days. On our first day we drove into a flash flood. Note the photo of the chocolate waterfall. It was quite spectacular. The next morning it was dry. The Fremont River was also a reddish brown and continued to rage the next morning.
Just east of the schoolhouse is a boardwalk over a marshy area along the Fremont River. This is a must see in Capitol Reef. I've been a few places with petroglyphs, but the petroglyphs along the boardwalk are the best I've personally visited and rival some of the best I've seen on HAZ.