He studied medicine in Bonn, Strasbourg, and Halle. His instructors included Eduard Friedrich Wilhelm Pflüger (1829-1910), Bernhard Naunyn (1839-1925), Oswald Schmiedeberg (1838-1921), and Joseph von Mering (1849-1908), and from 1897 to 1905 he worked at the university medical clinic at Giessen under Franz Riegel (1843-1904). In 1905 he became head of the medical department at the city hospital in Dortmund, and in 1908 director of the Krankenanstalt in Mannheim. Afterwards he was a professor at Halle an der Saale (1918) and Frankfurt am Main (1927).
Volhard made several important contributions in the fields of cardiology and nephrology. He is especially remembered for his collaboration with pathologist Karl Theodor Fahr (1877-1945) in Mannheim concerning research of kidney diseases. The two physicians created a classification system of renal disorders, in which they made the differentiation between degenerative (nephroses), inflammatory (nephritides) and arteriosclerotic (scleroses) diseases. With Fahr he published a classic monograph on Bright's disease called Die Bright'sche Nierenkrankheit, Klinik, Pathologie und Atlas.
Volhard recognized that constrictive pericarditis was a treatable condition, and as a result of his research with Viktor Schmieden (1874-1945), it led to the first pericardectomy for constrictive pericarditis. Volhard also performed extensive studies regarding renovascular hypertension and uremia. Regarding uremia, he divided associated symptoms into two criteria called "true uremia" and "pseudo-uremia". Pseudo-uremia was described as having symptoms of independent origin, such as cases involving elevated arterial blood pressure.
In 1903, Volhard was credited with the discovery of lipase in the heart and kidney. He also developed a method of preserving cardiac specimens via a process of dehydration and the application of hot paraffin. In Berlin, the Franz-Volhard-Klinik is named after him.