Piton de la Fournaise is one of the most active worldwide volcanoes, located on the southeastern part of La Réunion Island. In this work, we focus on the eruption that occurred on the southeastern flank of this volcano, inside the Enclos Fouqué caldera, from 11 to 15 August 2019. This distal event was characterized by the opening of two eruptive fissures and accompanied by shallow volcano–tectonic earthquakes. We exploit the ground displacements using Sentinel-1 Differential Interferometric Synthetic Aperture Radar (DInSAR) measurements, which include the ground deformations generated during both the pre- and co-eruptive phases. To investigate the sources responsible for the detected ground displacements, we perform an analytical modeling of the retrieved DInSAR measurements. Our results reveal the presence of five volcanic sources (i.e., one sill-like source and four dikes), whose concomitant action during the pre- and co-eruptive phases generated the complex detected deformation pattern. The retrieved volcanic sources correlate well with the location of the opened fissures, the spatial distribution and the temporal evolution of the recorded seismicity, and other geophysical evidence already known in the literature.