Franz studied organ at Dessau from 1835 to 1837. Later he returned to Halle, where he became a friend of Wilhelm Osterwald, many of whose poems he set to music. About the time he published his first songs (1843) he began to become deaf; nonetheless, he became organist at the Ulrichs Church, then conductor of the city's Singakademie, and, finally, musical director at Halle University, where he was made a doctor of music in 1861. Increasing deafness and nervous disorders caused him to retire in 1868, and he was supported for the rest of his life by a singer, Arnold von Pilsach. Franz Liszt, Joseph Joachim, and other prominent musicians arranged concerts for his benefit in 1872. In his later years Franz arranged works by Johann Sebastian Bach, George Frideric Handel, Wolfgang Amadeus Mozart, and Schubert.

His songs, of which there are about 350, are remarkable for their sensitive musical prosody. About a quarter are to texts by Heinrich Heine. Most of his songs are strophic, with the music repeated after each verse, and were written for a mezzo-soprano of limited range. Among them are “Lullaby,” “Stormy Night,” and “Dedication.” He also wrote a few choral and religious works.