Woven fabrics have multiple structural, aesthetic, and medical applications that require knowledge of their mechanical properties. While isolated fiber properties are easily determined, bulk properties of woven material, which can be coated or locally reinforced, require knowledge of yarn density, weave style, and other characteristics that are difficult to obtain experimentally. Additionally, fiber rearrangement, twist, yarn contact, and fiber-direction coupling result in non-linear mechanical responses. As a result, there is no universal material model for woven materials, and each fabric requires a specific model and parameter calibration. Recently, methods to simultaneously discover material models and their parameters from experimental or synthetic datasets have been proposed. Here, we use automated model discovery to simultaneously extract the material model and its parameters from biaxial test data of a TPU-coated woven nylon fabric. We show that Constitutive Artificial Neural Networks discover a sparse three-term hyperelastic material law with one isotropic and two anisotropic contributions, reproducing the measured biaxial response with a mean $R^2=0.97$. Across 20 initializations, predictive accuracy remains robust despite variations in the exact sparse representation, consistent with strong correlations between several candidate terms. LARS-LASSO independently recovers the same dominant constitutive contributions at approximately 100-fold lower computational cost. These results are directly applicable to numerical finite-element models of fabric-based structures, including soft robotic devices. More broadly, these results provide a foundation for further model discovery, improved constitutive modeling, and mechanistically informed optimization of woven fabric structures.

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