Reinjection of produced water is a critical aspect of managing geothermal reservoirs. The sustainability of extracted thermal energy relies on the performance of well doublets, which in turn is linked to the hydrothermal properties of the reservoir, the thermal characteristics of confining layers, and operating conditions. This study presents an advanced mixed-hybrid finite element simulator that solves coupled hydrothermal equations on unstructured grids. The model is favorably compared with the conforming finite element method at a geothermal power plant site that exploits the Dogger reservoir in the Paris basin. The study also includes a parametric sensitivity analysis, using an ensemble simulation to assess doublet lifetime, thermal breakthrough, and their ratio as performance metrics. Our findings emphasize the significant influence of horizontal permeability anisotropy and production flow rate on doublet performance, with doublet orientation relative to the principal axes of the areal permeability tensor as a key control parameter. Other influential factors include the thermal conductivity of the confining beds, while longitudinal thermal dispersivity and the total productive thickness of the reservoir are less critical. We establish, for the first time, a simple relationship between doublet lifetime and thermal breakthrough, indicating that the former is twice as long as the latter. This underscores the importance of long-term monitoring to sustain geothermal exploitation. This relationship can inform enhanced management of the Dogger reservoir at the basin scale.