Solich grew up in Cleveland, Ohio, and graduated from Holy Name High School in 1962, where he earned all-state, All-America, and all-scholastic honors. He was a part of Bob Devaney’s first recruiting class at Nebraska, and became a standout for the Huskers in the mid-1960s, where he earned the nickname "Fearless Frankie". An All-Big Eight fullback and co-captain of the Huskers’ 1965 team, his playing career earned him induction into the Nebraska Football Hall of Fame in 1992. In NU's 27–17 win over Air Force in 1965, he ran for 204 yards on 17 carries, becoming the first Husker to run for 200 yards in a game, and subsequently the first Husker to be featured on the cover of Sports Illustrated.