Madsen was a member of the BYU School of Music Faculty from 1919-1952. Both he and his wife, Florence Jepperson Madsen, had a large impact on the students that they were able to teach and lead in choirs.
He was a member of the Mormon Tabernacle Choir and served as a missionary in Denmark and Norway. He was the supervisor of music in the Jordan and Nebo School Districts and taught high school music.
At the dedication of the Harris Fine Arts Center, a recital hall was named in honor of Franklin and his wife.
- Special Program for Naming of Areas, Franklin S. Harris Fine Arts Center. Tuesday, November 23, 1965 at Brigham Young University, Provo, UT 84602.
- Waterstradt, Jean Anne, ed., They Glady Taught: Ten BYU Professors, Brigham Young University and the Emeritus Club, 1987, volume II, pp. 98-137.