Two-dimensional transition metal carbides and nitrides (MXenes) have attracted extensive attention due to their layered structure and tunable photophysical properties. However, the optical response and electronic structure origin of rare-earth lanthanide-based MXenes remain poorly understood. Based on density functional theory, combined with phonon spectroscopy and ab initio molecular dynamics (AIMD) to evaluate the structural stability of La₂CF₂ monolayer, and using HSE06 hybrid functional level calculations to assess its electronic structure and optical properties, and further using the deformation potential theory to calculate its carrier mobility. The results show that La₂CF₂ has a hexagonal structure, the phonon spectrum has no imaginary frequency and the AIMD energy and temperature fluctuate stably at 300 K, verifying its dynamic and thermodynamic stability. La₂CF₂ exhibits direct bandgap semiconductor characteristics, the valence band top is mainly contributed by C/F-p states, the conduction band bottom is mainly dominated by La-d states, and the CBM and VBM show different spatial charge distribution characteristics. Based on the deformation potential theory calculation, the carrier transport of La₂CF₂ has certain in-plane anisotropy, and the theoretical mobility under the limitation of acoustic phonon scattering is at the order of 10² cm²·V^-1·s^-1. Optical calculations show that La₂CF₂ has wide-spectrum strong absorption in the visible-ultraviolet region.