We present a new automated earthquake detection and location method based on beamforming (or back projection) and template matching, and apply it to study the seismicity of the Southwestern Alps. We use beamforming with prior knowledge of the 3D variations of seismic velocities as a first detection run to search for earthquakes that are used as templates in a subsequent matched-filter search. Template matching allows us to detect low signal to noise ratio events, and thus to obtain a high spatiotemporal resolution of the seismicity in the Southwestern Alps. We describe how we address the problem of false positives in energy-based earthquake detection with supervised machine learning, and how to best leverage template matching to iteratively refine the templates and the detection. We detected 18,754 earthquakes over one year (our catalog is available online), and observed temporal clustering of the earthquake occurrence in several regions. This statistical study of the collective behavior of earthquakes provides insights into the mechanisms of earthquake occurrence. Based on our observations, we infer the mechanisms responsible for the seismic activity in three regions of interest: the Ubaye valley, the Briançonnais and the Dora Maira massif. Our conclusions point to the importance of fault interactions to explain the earthquake occurrence in the Briançonnais and the Dora Maira massif, whereas fluids seem to be the major driving mechanism in the Ubaye valley.