The generation of a highly permeable fracture network in Enhanced Geothermal Systems (EGSs) is a prerequisite to develop such geothermal reservoirs efficiently. However, it lacks a quantitative geometrical metric to evaluate what kind of fracture network is preferable for geothermal production. To address this problem, we use our previously developed high-fidelity Thermo-Hydro-Mechanical (THM) coupling model to investigate the joint influence of fracture geometry and thermal stress on the THM behaviors of EGSs. Results show that the geometrical connectivity of fracture networks plays a dominant role in determining the THM processes and the thermal performance of EGSs, in which the network connectivity integrates multiple properties of fracture networks including the fracture length, intensity, location and orientation. Satisfactory thermal performance tends to be achieved when the connectivity of fracture systems ranges from 15 to 35. We focus on such fracture networks and design an appropriate production scenario for optimizing multiple objectives (i.e. maximum EGS service life, heat extraction rate, and global thermal power). The overall heat extraction performance of EGSs under the optimum scenario gets improved by 77.7% compared with the base case. This research provides an effective workflow and feasible methods for evaluating and optimizing energy exploitation efficiency of EGSs.