In this paper we want to identify features of mathematical activity in France during the interwar period and to bring out effects of the First World War, avoiding the reconstructions and necessarily partial images proposed by some of the protagonists who followed their own mathematical ideas and interests. We choose to focus on the mathematicians who held positions of institutional authority in the French mathematical community and thus exerted a decisive influence on the mathematical scene of their time. First we identify and characterize the group of those academicians, professors at the Sorbonne, members of the examining boards of doctoral dissertations. Secondly, we briefly analyze the activity of the most powerful among these mathematicians and reveal mathematical domains and norms that historiography has usually considered as outmoded, marginal or has simply ignored. We finally propose a new view of the French mathematical scene of this period, a view which is much more complex, diverse and less severe than the one usually given.