Bouré was born in Brussels as the Belgian war of independence was drawing to a close. He studied locally first under Guillaume Geefs and then from 1846 to 1852 under Eugène Simonis at the Royal Academy for Fine Art, going abroad to complete his training at the Academy of Fine Arts at Florence. In his studies, he followed the same course as his older brother, Paul Bouré. Paul died in his mid-twenties when Antoine-Félix was only 17.