A grandson of geologist Louis Cordier and a great-nephew of politician and scientist Louis Ramond de Carbonnières, Henri Cordier pursued studies at the École Libre des Sciences Politiques, founded in 1872, where he received high honors. He was first attracted by the Pyrenees, to which he traveled in 1874, before visiting the Swiss Alps the following year. His brief Alpine career combined talent and audacity. In the 1876 season he succeeded in making eleven first ascents. He claimed to have climbed the western peak of the Meije that year, but was subsequently forced to retract the claim.