In 1889 he received his medical doctorate, and in 1909 became a professor of clinical surgery in Paris. Delbet is remembered for his advocacy of magnesium chloride. During World War I, Delbet was searching for a solution that could cleanse wounds but not damage tissue as traditional antiseptics did.
In 1915 he found that magnesium chloride not only worked as an antiseptic, but was also harmless to body tissue.
Serendipitously, he discovered that when the magnesium chloride solution was taken orally or intravenously, it appeared to be a remedy for other ailments. Delbet also believed that magnesium was beneficial to the efficiency of white blood cells, of which he described in his treatise "Politique Préventive du Cancer".
With Jean-François-Auguste Le Dentu (1841-1926) and others, he was co-publisher of the multi-volume Traité de chirurgie clinique et opératoire (1901 et seq).