Wallace was the son of John Andrew and Helen Smith Beeckman Graham.
Wallace married Victoire Marie Binsse. on July 7, 1874, in Watertown, New York. Marie was the daughter of Dr. John Binsse, of Watertown.
Wallace spent the early years of his education in France, and completed his education at the United States Naval Academy at Annapolis. He spent two years on the battle ship Michigan before being assigned, as a navigator, aboard the U.S.S. Juanita. Three days after his assignment Wallace died of pneumonia.
Wallace received full military honors, after serving 15 years in the navy.