Summary
This paper studies the distribution and dynamics of profitability among French non-financial corporations between 1906 and 1952, using more than 50,000 firm-year observations. We ask whether capital reallocation generates the turbulent arbitrage process documented for modern economies, in which firms continually change position while profitability follows a stable ergodic distribution. In the raw historical data, this benchmark is strongly rejected. The failure, however, is highly structured. Profitability can be decomposed into a common time-varying centre, persistent firm-specific profitability positions, firm-specific fluctuation scales, and a standardized residual component. Among long-lived corporations, only the joint removal of aggregate historical variation and firm-specific location and scale recovers an approximately Laplace distribution. Monte Carlo-adjusted tests likewise show that apparent violations of ergodicity largely disappear under this normalization, including under blocked cross-fitting and conservative robustness checks. Firm-specific profitability regimes remain substantially persistent over horizons of roughly twenty-five years, but evolve sufficiently to rule out permanently fixed firm parameters. The evidence therefore rejects a single ergodic distribution of profitability in levels, while revealing a common stochastic law conditional on historical conditions and persistent local firm regimes. French capitalism in this turbulent period appears to exhibit not global ergodicity, but a structured form of profitability dynamics in which common reallocation regularities coexist with persistent firm heterogeneity and historical change.