In this paper, we document whether and how much the equalizing force of earnings mobility has changed in France in the 1990s. For this purpose, we use a representative three-year panel,the French Labour Force Survey. We develop a model of earnings dynamics that combines a flexible specification of marginal earnings distributions (to fit the large cross-sectional dimension of the data) with a tight parametric representation of the dynamics (adapted to the short timeseries dimension). Log earnings are modelled as the sum of a deterministic component, an individual fixed effect, and a transitory component which is assumed first-order Markov. The transition probability of the transitory component is modelled as a one-parameter Plackett copula. We estimate this model using a sequential EM algorithm. We exploit the estimated model to study employment/earnings inequality in France over the 1990-2002 period. We show that, in phase with business cycle fluctuations (a recession in 1993 and two peaks in 1990 and 2000), earnings mobility decreases when cross-section inequality and unemployment risk increase. We simulate individual earnings trajectories and compute present values of lifetime earnings over various horizons. Inequality presents a hump-shaped evolution over the period, with a 9% increase between 1990 and 1995 and a decrease afterwards.Accounting for unemployment yields an increase of 11%. Moreover, this increase is persistent, as it translates into a 12% increase in the variance of log present values. The ratio of inequality in present values to inequality in one-year earnings, a natural measure of immobility or of the persistence of inequality, remains remarkably constant over the business cycle.