This study aims to explore two-dimensional semiconductor materials with superior carrier transport properties to address the growing demands of high-speed electronics and optoelectronic devices. The focus lies on evaluating the feasibility of monolayer FeGa₂S₄ as a candidate material through systematic theoretical investigations. First-principles calculations were employed to analyze the exfoliation energy of FeGa₂S₄ bulk crystal and the structural stability, mechanical properties, and strain-dependent optoelectronic behavior of its monolayer counterpart. Strain engineering strategies, including uniaxial and biaxial strain, were applied to assess carrier mobility modulation and spectral response. Our calculation results indicate that monolayer FeGa₂S₄ is an indirect bandgap semiconductor (E_g =1.65 eV) with low stiffness (Young's modulus up to 151.6 GPa) and high flexibility (Poisson's ratio less than 0.25), demonstrating exceptional thermodynamic stability. Under +5% uniaxial tensile strain, its electron mobility along x/y directions dramatically increases to 5402.4/4164.0 cm²·V^-1·s^-1, fivefold higher than its hole mobility. Biaxial strain outperforms uniaxial strain in bandgap modulation and induces systematic redshift in optical spectra, significantly enhancing visible-light harvesting efficiency. This work reveals that monolayer FeGa₂S₄ is a promising highmobility photoactive material for next-generation solar cells and optoelectronics. The strain-mediated control of electronic and optical properties provides a theoretical framework for optimizing 2D semiconductors, offering critical guidance for experimental synthesis and device engineering. These findings highlight the material's potential for advancing energy conversion technologies and photonic applications.