Delpech's work includes the first account of rhinoplasty in France. On 4 June 1823, Delpech performed the first of six cases of rhinoplasty by the Indian forehead flap method, and one (unsuccessful) with a flap from the arm following von Graefe (No. 5738). Delpech also was the first to restore the lower lip by means of a skin graft from the throat.

Delpech devoted pp. 147-231 of vol. 1 to Considerations sur la difformité appelé pied-bots. In this he described on pp. 184-192 the beneficial effect of section of the tendo Achillis for club-foot; he performed the operation on May 9, 1816, and although not first to do so, he was the first to demonstrate the value of tenotomy in the correction of contracture deformities of the extremities.