Antoine Bessems was born in Antwerp, at the time part of the United Kingdom of the Netherlands, then under French control. Bessems entered the Paris Conservatory, studying the violin with Pierre Baillot. After graduating, he pursued a career as a performer, mainly in Paris. He also served as conductor of the Philharmonic Orchestra of Antwerp for a number of years. His last years were spent in Paris where he became a prominent teacher and performer.