Distelmans's father was a shoemaker who dreamed of training his children to be musicians. Distelmans's mother died while giving birth to her sixth child, and the children's father raised them to play in a string quartet. As a young man, Napoleon won the prestigious Prix de Rome viola, which awarded him a scholarship to study with one of the leading viola players of this era in London.
The language of study at the Antwerp Conservatory had just been changed from French to Dutch at the instigation of Flemish nationalist composer Peter Benoit when the Distelmans brothers enrolled there. The school remained a breeding ground for Flemish nationalism long afterwards. The cello-playing brother of the quartet particularly became a fierce nationalist, which contributed to the dissolution of the quartet during World War II.