The fracture connectivity in enhanced geothermal systems plays a vital role in the process of heat extraction. In this paper, a coupled thermo-hydro-mechanical model with discrete fractures is developed to investigate the influence of fracture connectivity on the heat extraction performance of a geothermal doublet system. The proposed model adopts the assumptions of a one-dimensional fracture element and thin elastic layer. The influences of spacing or connectivity of two discrete fractures on heat extraction efficiency are investigated under varying thermal conductivity and permeability ratios. The evolutions of fracture aperture, production temperature, and heat extraction rate are analyzed. The simulations indicate that the key factors influencing thermal recovery, listed in order of decreasing impact, are the permeability ratio, fracture connectivity, and bedrock thermal conductivity. When the permeability ratio exceeds 10−6, thermal convection becomes the dominant factor, thereby diminishing the impact of fracture connectivity. In contrast, when the bedrock thermal conductivity is greater than 3 W/(m·K), thermal conduction takes precedence, and the efficiency of geothermal heat extraction is enhanced by the preferential flow paths resulting from fracture connectivity. The research results have important guiding significance for the optimization design of production strategy in the heat extraction process of enhanced geothermal reservoirs.