 Cellier was born in South Hackney, London, the youngest of the five children of Arsène Cellier, a language teacher from France, and his wife Mary Ann Peterine, formerly Peacock, "né" Thomsett.He followed his eldest brother Alfred as a chorister at the Chapel Royal, St James's.Like his brother and the latter's fellow pupil Arthur Sullivan, François benefited from the tutelage of the Rev Thomas Helmore, who ensured that the choristers received an all-round education in addition to their musical training.