His father was the business partner of his maternal grandfather in lace manufacturing, a traditional industry in Calais.
Just prior to the start of World War II he received his baccalauréat, and went to Ambert to begin preparing for the exam for entering a grande école. Later on he moved from Ambert to Grenoble to complete his preparation, both being in the so-called "Free Zone" during World War II.
In 1941 he was admitted to the École Normale Supérieure in Paris, along with Marcel Boiteux. He was influenced by Henri Cartan and the Bourbaki writers. When he was about to take the final examinations in 1944, D-Day arrived and he instead enlisted in the French army. He was transferred for training to Algeria and then served in French occupational forces in Germany until July 1945.
Debreu passed the Agrégation de Mathématiques exams at the end of 1945 and the beginning of 1946. By this time he had become interested in economics, particularly the general equilibrium theory of Leon Walras. From 1946 to 1948, he was an assistant in the Centre National de la Recherche Scientifique. During these two and a half years he made the transition from mathematics to economics.
In 1948, Debreu came to the USA on a Rockefeller Fellowship which allowed him to visit several American universities, as well as those in Uppsala and Oslo in 1949-50. Debreu began working as a Research Association and joined the Cowles Commission at the University of Chicago in the summer of 1950.
There he remained for five years, returning to Paris periodically. In 1954 he published a breakthrough paper titled Existence of an Equilibrium for a Competitive Economy (together with Kenneth Arrow), in which they provided a definitive mathematical proof of the existence of general equilibrium, using topological rather than calculus methods.
In 1955 he moved to Yale University. In 1959 he published his classical monograph, Theory of Value: An Axiomatic Analysis of Economic Equilibrium, (Cowles Foundation Monographs Series), which is one of the most important works in mathematical economics. He also studied several problems in the theory of cardinal utility, the additive decomposition of a utility function defined on a Cartesian product of sets.
In this monograph, Debreu sets up an axiomatic foundation for competitive markets. He establishes the existence of equilibrium using a novel approach. The main idea is to show that there exists a price system for which the aggregate excess demand correspondence vanishes. He does so by proving a type of fixed point theorem based on the Kakutani fixed point theorem. In Chapter 7 of the book Debreu introduces uncertainty and shows how it can be incorporated into the deterministic model. Here he introduces the notion of a contingent commodity, which is a promise to deliver a good should a state of nature realize. This concept is very frequently used in financial economics as a so called Arrow Debreu security.
In 1960-61, he worked at the Center for Advanced Study in the Behavioral Sciences at Stanford and devoted mostly to the complex proof that appeared in 1962 of a general theorem on the existence of an economic equilibrium.
In January 1962, he started worked at the University of California, Berkeley where he held the title University Professor and Class of 1958 Professor of Economics and Mathematics Emeritus. During his leaves in late sixties and seventies he visited universities in Leiden, Cambridge, Bonn, and Paris.
His later studies centred mainly on the theory of differentiable economies where he showed that in general aggregate excess demand functions vanish at a finite number of points. Basically, showing that economies have a finite number of price equilibria.
In 1976 he received the French Legion of Honor. He was awarded the 1983 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for having incorporated new analytical methods into economic theory and for his rigorous reformulation of general equilibrium theory. He was member of the International Academy of Science.
In 1990, he served as President of the American Economic Association.
Debreu married Françoise Bled in 1946 and had two daughters, Chantal and Florence, born in 1946 and 1950 respectively.