Schmitz was born in Eupen and attended gymnasium in Aachen. He lost his right arm in an accident at the age of 10, but nonetheless excelled academically. He studied at the University of Bonn, where he earned a PhD, and was in particular influenced by Barthold Georg Niebuhr; Schmitz later published in England a collection of notes taken from Niebuhr's lectures as Lectures on Roman History (1844).
He married an English woman, and moved to England in 1837; around 1840 they had a daughter, Leonora Schmitz, who would become a noted music critic. He became associated with a number of scholars there, writing many of the mythological entries for classicist William Smith's Dictionary of Greek and Roman Biography and Mythology, and serving as "a key figure in the transmission of German classical scholarship to Victorian Britain".
Schmitz moved to Scotland in 1846 to serve as rector of the Royal High School in Edinburgh from that year until 1866. In his induction speech he expressed the hope that his appointment would be "the means of strengthening and increasing the intellectual sympathy which has so long existed between this country and Germany". In that office in 1859 he also tutored HRH The Prince of Wales in Roman history.
Schmitz moved back to England in 1866, serving as Principal of London International College from 1866 to 1874, and Classical Examiner at the University of London from 1874 to 1884. He was granted a civil list pension of £50 in 1881, doubled in 1886.
- Edmund Burke, ed. (1891). "Obituary: May". The Annual Register: A Review of Public Events at Home and Abroad for the Year 1890. pp. 158–159.
- David Baptie (1894). "Young, Mrs. John (née Leonora Schmitz)". Musical Scotland, Past and Present. p. 205.
- Nick Lowe (2005-12-20). "Killing the Graves Myth". The Times Online. Retrieved 2010-10-20.
- John Murray, A History of the Royal High School (Edinburgh: Royal High School, 1997), p. 50.
- Murray, History, p. 53.