This paper presents Léon Walras and Augustin Cournot views on monetary regulation. Important differences can be found in their views about the convenience of the issuing of paper money and fiat money in general. Whereas Walras is against bank notes, even if coming from a central bank, Cournot has a moderate position. He accepts the need for bank notes even without a strict adjustment to metal reserves. It can be ascertained that Cournot believes discretionary monetary regulation is convenient and acceptable, while Walras believes the only acceptable monetary system is one based exclusively on the stability of the value of money under a monetary rule following the strict equivalence between metallic reserves and a pure medium of exchange form of money. This paper shows Cournot’s ability to understand more clearly than Walras the evolution of the monetary system of his days. Whereas Walras is trying to guarantee the coherence of his pure theory with his applied theory, and he is then unable to accept the evolution toward a monetary system based on fiat money and he proposes very rigid and complex system of quasi-bimetallic circulation where banks are simple mediators between entrepreneurs and savings.