In gas-bearing coal seam mining projects, the pivotal considerations encompass the assessment of gas migration, emission trends, and coal seam stability, which are crucial for ensuring both the safety and efficiency of the project. The accurate evaluation of the nonlinear evolution of the fracture network, acting as the primary conduit for gas migration and influenced by mining disturbances, coal seam stress, overlying strata pressure, and gas pressure, emerges as a key determinant in gauging coal seam stress and safety. To address the industry challenge of quantitatively assessing the complex behaviors of fracture networks during gas-bearing coal seam extraction, this study introduces a novel, interdisciplinary fractal analysis model. Drawing upon fractal theory for classical porous media, four fractal parameters capable of quantitatively characterizing the microscopic behaviors of fractures are proposed and defined as functions of permeability. Subsequently, the gas pressure in gas-bearing coal seams, coal seam deformation and stress, in-situ stress, overlying strata pressure, and adsorption–desorption effects are comprehensively coupled and applied to the classic gas-bearing coal seam at the Jianxin Coal Mine’s 4301 working face in Shaanxi, China. Upon the robust validation of the proposed model, the present computational results reveal: (1) the proposed micro-parameters adeptly characterize the number, roughness, tortuosity, and length of fractures in gas-bearing coal seams; (2) a larger fractal dimension of fractures leads to increased coal seam stress and strain, while the fractal dimensions of fracture tortuosity and roughness are inversely proportional to coal seam stress and strain; (3) these fractal parameters directly induce evolutionary changes in gas seepage behavior, leading to varying degrees of mechanical property evolution in the coal seam. When $D_S$ and $D_T$ increased from 1.2 to 1.8, the maximum change in coal seam deformation was 16.9% and 13.8%, respectively, and when $𝜀$ increases from 0.03 to 0.12, the coal seam deformation changes by 15.1%. This represents a quantitative characterization unattainable by previously published coal seam analysis models, including mainstream fractal computation models.