This study presents a comprehensive two-step finite element (FE) homogenisation approach for predicting the effective elastic properties (EEP) of basalt fiber-reinforced epoxy textile composites in both plain and twill weave architectures. The methodology combines micro-scale analysis, using three-dimensional representative volume elements (RVEs) with hexagonal fiber packing, and meso-scale modeling using TexGen, enabling hierarchical multiscale evaluation of composite behavior. The developed micro-scale FE model is compared with other micromechanical models viz. Chamis model, Mori–Tanaka (Digimat-MT), Multiscale Designer (MSD), and Mechanics of Structure Genome (MSG) and found to be in good agreement along various fiber volume fraction values. Increasing fiber volume fraction (FVF) enhances the stiffness and shear resistance of the yarn. Using the validated yarn properties, Meso-scale homogenisation provided composite-level predictions closely aligned with benchmark models, with deviations typically within 1.5% to 4%. Extensive parametric studies revealed the critical influence of yarn spacing, yarn width, fabric thickness, and composite fiber volume fraction on mechanical performance. Notably, twill weave composites consistently outperformed plain weaves, attributed to smoother yarn trajectories and reduced crimp, with enhanced stiffness and shear moduli. The developed two-scale FE homogenisation strategy is computationally efficient and reliable, offering valuable insights for optimizing the design and structural application of basalt-epoxy textile composites in the automotive, aerospace, and civil engineering sectors.