We study changes in effective stress (normal stress minus pore pressure) that occurred in the French Alps during the 2003-2004 Ubaye earthquake swarm. Two complementary data sets are used. First, a set of 974 relocated events allows us to finely characterize the shape of the seismogenic area and the spatial migration of seismicity during the crisis. Relocations are performed by a double-difference algorithm. We compute differences in travel times at stations both from absolute picking times and from cross-correlation delays of multiplets. The resulting catalog reveals a swarm alignment along a single planar structure striking N130°E and dipping 80°W. This relocated activity displays migration properties consistent with a triggering by a diffusive fluid overpressure front. This observation argues in favor of a deep-seated fluid circulation responsible for a significant part of the seismic activity in Ubaye. Second, we analyze time series of earthquake detections at a single seismological station located just above the swarm. This time series forms a dense chronicle of +16,000 events. We use it to estimate the history of effective stress changes during this sequence. For this purpose we model the rate of events by a stochastic epidemic-type aftershock sequence model with a nonstationary background seismic rate λ0(t). This background rate is estimated in discrete time windows. Window lengths are determined optimally according to a new change-point method on the basis of the interevent times distribution. We propose that background events are triggered directly by a transient fluid circulation at depth. Then, using rate-and-state constitutive friction laws, we estimate changes in effective stress for the observed rate of background events. We assume that changes in effective stress occurred under constant shear stressing rate conditions. We finally obtain a maximum change in effective stress close to −8 MPa, which corresponds to a maximum fluid overpressure of about 8 MPa under constant normal stress conditions. This estimate is in good agreement with values obtained from numerical modeling of fluid flow at depth, or with direct measurements reported from fluid injection experiments.