Guillaume was married in 1888 to A.M. Taufflieb, with whom he had three children.
Guillaume is also known for the earliest estimation of the "radiation of the stars” in his 1896 paper "La Température de L'Espace (The Temperature of Space)". This is the first known reference to the concept that would later be known as the Cosmic Microwave Background.
Guillaume was head of the International Bureau of Weights and Measures. He worked with Kristian Birkeland, serving at the Observatoire de Paris—Section de Meudon. He conducted several experiments with thermostatic measurements at the observatory. He was the first to determine accurately the temperature of space.
