He studied medicine at the University of Utrecht, and trained as pathologist in Amsterdam. During this time he came across the symptoms of what is now known as domestic Pompe disease, or Glycogen storage disease type II, which he described in his 1932 publication Over idiopathische hypertrophie van het hart. On December 27, 1930, Dr. Pompe had carried out an autopsy on a 7-month old girl who had died of unknown causes. He found the enlarged heart now known to be characteristic of the infantile form of the disease and had some microscope slides prepared. These showed that the muscle tissue was distorted into an pentagonal mesh. 
He was executed by the Nazis in 1945 because of espionage. His older brother was Professor Willem Pompe who was a prominent criminologist at the University of Utrecht and namesake of the Willem Pompe institute.
^Kroos M, Pomponio RJ, van Vliet L, et al. (June 2008). "Update of the Pompe disease mutation database with 107 sequence variants and a format for severity rating". Hum. Mutat.29 (6): E13–26. doi:10.1002/humu.20745. PMID18425781.
^Pompe J-C. Over idiopatische hypertropie van het hart. Ned Tijdscr Geneeskd 1932; 76:304.