Recently, bournonite (CuPbSbS₃) has been identified as a potential ferroelectric photovoltaic (PV) material with a 1.3 eV band gap, which falls in an appropriate range for single-junction PV devices. Progress in applying bournonite has yielded several studies reporting successful thin-film processing, the most recent of which demonstrated a 2.65% power conversion efficiency for a bournonite-based PV device. In an effort to explore bournonite band gap engineering for PV and other prospective applications (e.g., thermoelectric, spintronic), we here consider the solid-state synthesis of selenium-alloyed bournonite, CuPbSb(S_1–xSe_x)₃, across the full range of x (0.0 ≤ x ≤ 1.0) and report phase purity for 0.0 ≤ x ≤ 0.5. We characterize the crystal structure and band gap of the samples using X-ray diffraction and diffuse reflectance spectroscopy, determining a band gap decrease for single-phase samples from 1.25 eV at x = 0.0 to 1.06 eV at x = 0.5. Formation energies determined using dispersion-corrected hybrid density functional theory (DFT) support experimental findings and are consistent with the stability (instability) of the x = 0.5 (x = 1.0) structure relative to starting materials. The computed band structures show a decreasing trend in the band gap with increasing x, again consistent with experiment, with the states at the conduction (valence) band minima (maxima) being principally derived from Pb (S/Se) states. Spin texture analysis and detailed comparison of spin splitting parameters show that Se alloying modifies the band gap while maintaining Rashba spin splitting character within the electronic structure. Rashba splitting is most pronounced for the conduction band minimum along the Γ–X path in the Brillouin zone. Energy separation between spin states is maintained at ΔE ∼0.2 eV for the various Se contents, with σ_z as the spin direction. A smaller spin splitting occurs along Γ–Z (decreasing value with increasing x), with σ_x as the spin direction.