Brallier was born in Cherry Tree, Pennsylvania, near Indiana. He was the son of Dr. Emanuel Brallier, a physician, and his wife, Lucy M. Kinport Brallier. His grandparents were from Alsace-Lorraine, accounting for the French-sounding name. As a boy, Brallier remembered having worked in a glass factory. His first recollection of football was in 1890, at the age of 13, playing in high school for the West Indiana Public School team. By his sophomore year in 1892, he was the captain and right halfback.