The integration of ferroelectric barriers into high-temperature Josephson junctions offers a pathway to tunable superconducting quantum devices. Here, we demonstrate robust Josephson coupling in YBa2Cu3O7-x (YBCO)/Bi0.5Na0.5TiO3 (BNT)/YBCO trilayer junctions incorporating a 40 nm ferroelectric BNT barrier. Epitaxial trilayers were fabricated by pulsed laser deposition on SrTiO3 substrates and investigated under broadband terahertz (THz) irradiation (0.5-2.5 THz). At 1.5 THz, close to the Josephson plasma resonance, the BNT polarization increased from 33.4 to 46.4 uC/cm2 at 30 K, enhancing superconducting transport. The junctions exhibited a well-defined zero-voltage supercurrent branch, with the critical current Ic(T) remaining nearly constant up to 60 K and reaching 468.2 uA under 1.5 THz excitation, evidencing strong phase coherence. Scanning tunneling spectroscopy revealed an enhanced superconducting gap in YBCO/BNT/YBCO (Delta = 1.3 meV) compared with pure YBCO (Delta = 1.05 meV), while optical conductivity measurements showed a reduction in conductivity and gap with increasing temperature, consistent with BCS theory under THz excitation. Atomic force microscopy and X-ray reflectivity confirmed uniform morphology and sharp interfaces, excluding defect-mediated transport. Magnetic field modulation of Ic(B) exhibited a canonical Fraunhofer interference pattern, and resistance mapping revealed alternating lobes of high and low dissipation, indicating coherent Josephson tunneling. These results establish that Josephson coupling is intrinsic to the YBCO/BNT/YBCO junctions, enabled by the dipolar character and dynamic THz response of the BNT barrier. This study identifies BNT as a viable, tunable barrier material for next-generation high-Tc superconducting quantum devices.