Employing multi-stage fracturing technology in horizontally accessed wells is a well-known way to successfully develop shale reservoirs. The interaction between natural fractures and hydraulic fractures has a significant impact on the fracturing effect. In this study, a coupled model of rock deformation and fluid flow was established using the cohesive zone method to simulate the propagation of hydraulic fractures under the synergistic effect of natural fractures and wellbore interference. The influence of in situ stress, fracture spacing, the number of fracture clusters, and the fracturing methods on the formation of fracture networks was analyzed. Studies on the fracture morphology and connectivity of fracture networks show that when the in situ stress difference is small, multiple fractures can easily form, and when the in situ stress difference is large, they can easily gather into a single fracture. An excessive reduction in fracture spacing may impede the optimal propagation and interconnection of hydraulic fractures. The findings reveal that augmenting the fracture spacing from 5 m to 8 m results in a significant 15.59% increase in the overall extent of fracture propagation. Moreover, it also adds to the complexity of the fracture network. Increasing the number of hydraulic fracturing clusters can improve the fracture length and fracture propagation complexity. When the number of fracturing clusters increased from two clusters to five clusters, the maximum fracture propagation width increased by 25.23%. Comparing sequential fracturing and simultaneous fracturing, the results show that simultaneous fracturing can form a more complex fracture network with better connectivity, which is conducive to increasing oil and gas production. The obtained results can provide a reference for horizontal well fracturing designs of shale reservoirs.