Franz was born in Guebwiller, the brother of the singer and pedagogue Julius Stockhausen, and son of the harp virtuoso Franz Stockhausen Sr. and his wife, the soprano Margarethe.
From 1860 to 1862 he studied at the Leipzig Conservatory under Ignaz Moscheles, Ernst Richter and Moritz Hauptmann.
From 1863 to 1866 he was chief conductor at Thann, in Alsace, and from 1866 to 1868 he was with his brother at Hamburg, who was then conducting the Philharmonic Concerts and the Singakademie.
In 1868 he became the conductor of the Société de Chant Sacré, and of Strasbourg Cathedral.
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