<p>This study presents a theoretical investigation into the tunable Goos–Hänchen (GH) shift in Floquet topological insulator (FTI) thin films when subjected to an off-resonant circularly polarized light. A key characteristic of these FTI thin films is their tunable bandgap, which can be dynamically adjusted by illuminating them with right- or left-handed circular polarization (RCP/LCP). The topological phases can be tuned by optical field strength and are classified by their Chern numbers. The Kubo formula is used to compute the optical conductivities in the FTI thin film. Using angular spectrum analysis, we derive a closed-form analytical expression for the GH shift. Our results reveal that the Hall conductivity in FTI thin films is highly sensitive to the intensity of the applied light field across various topological phases. We reveal that, far from the optical transition energies, the GH shift experiences substantial enhancement near the Brewster angle. Furthermore, we demonstrate that topological quantum phase transitions (TQPTs) influence the magnitude of the beam shifts, as well as the shifting of the Brewster angle, highlighting the GH shift as a promising tool for probing such transitions at the nanoscale. These findings offer valuable insights that could enable next-generation applications in topological photonics, quantum systems, and tunable optoelectronic technologies.</p>