While basal icequakes associated with glacier motion have been detected under Antarctica for several decades, there remains very little evidence of stick‐slip motion for Alpine glaciers. Here we analyzed 2357 basal icequakes that were recorded at Glacier d'Argentière (Mont‐Blanc Massif) between February and November of 2012 and that are likely to be associated with basal sliding. These events have been classified into 18 multiplets, based on their waveforms. The strong similarity of the waveforms within each multiplet suggests an isolated repeating source. Despite this similarity, the peak amplitude within each multiplet varies gradually in time, by up to a factor of 18. The distribution of these events in time is relatively complex. For long time scales, we observe progressive variations in the amplitudes of events within each multiplet. For intermediate time scales (hours), the events occur regularly in time, with typical return times of several minutes up to several hours. For short time scales (from 0.01 to 100 s), the largest multiplet shows clustering in time, with a power law distribution of the interevent times. The location of these events and their focal mechanisms are not well constrained, because most of these events were detected by a single seismometer. Nevertheless, the locations can be estimated with an accuracy of a few tens of meters using a polarization analysis. The estimated average depth of the basal events is 179 m, which is in good agreement with the estimated glacier thickness. The relative changes in distance between the source and the sensor can be measured accurately by correlating separately the P wave and S wave parts of the seismograms of each event with the template waveforms, which are obtained by averaging the signals within each multiplet. We observed small variations in the times between the P wave and the S wave of up to 0.6 ms over 50 days. These variations cannot be explained by displacement of the sensor with respect to the glacier but might be due to small changes in the seismic wave velocities with time. Finally, we found using numerical simulations that the observed signals are better explained by a horizontal shear fault with slip parallel to the glacier flow than by a tensile fault. These results suggest that the basal events are associated with stick‐slip motion of the glacier over rough bedrock. The rupture length and the slip are difficult to estimate. Nonetheless, the rupture length is likely to be of the order of meters, and the total seismic slip accumulated over one day might be as large as the glacier motion during the most active bursts.