We applied the double-difference tomography method to image the P and S-wave velocity structure of the European Hot Dry Rock geothermal reservoir (also known as the Soultz Enhanced Geothermal System) at Soultz-sous-Forets, France. We used absolute, differential catalog and differential cross-correlation times obtained from the reservoir's September and October 1993 hydraulic stimulations along with starting event locations obtained using Joint Hypocenter Determination and Collapsing methods. The stimulations produced over 12000 microseismic events of which we chose 8930 for further analysis. We obtained high accuracy cross-correlation differential times and then performed a double-difference tomographic inversion to jointly invert for velocity structure and event locations. It is shown through a detailed analysis of model and data residuals vs smoothing weight, ray path derivative weighted sums, and a synthetic checkerboard test that the double-difference inversion is able to produce interpretable results despite the poor source-receiver geometry employed in the study. The results show that velocity structure for S-waves correlates well with seismicity and show the expected low velocity zones at depths between 2900 and 3600 meters, where fluid was believed to have infiltrated the reservoir. P-wave velocity structure shows less of a correlation with seismicity and shows low velocity zones at shallow depths where no water was believed to have entered the reservoir. Between 2900 and 3600 meters the P-wave velocity structure shows high velocity zones near the injection well. The results also show the NNW-SSE trend of event location clusters and velocity structure which lines up with the maximum horizontal stress orientation. Lastly, we show that using the double-difference tomographic method to relocate events produces locations that come close to rivaling those of collapsing methods.