With Dastre, the "Dastre-Morat Law" is derived, a dictum which states that "the vasoconstriction of the capillaries of the body surface is usually accompanied by vasodilation of the internal vessels, especially of the viscera, and vice-versa".
Following his years spent in Paris, he became an instructor of physiology at the faculty of medicine in Lille.
In 1882 he was appointed professor of physiology at the faculty of medicine in Lyon, a position he maintained until his retirement in 1916.
Morat had a keen interest in the field of surgery, being credited for introducing a process of administering morphine and atropine to a patient prior to the administration of anesthesia.