Band gap tuning of titanium based perovskite oxides through chalcogen doping is an attractive avenue for realizing visible light driven photocatalysis for hydrogen production. Unfortunately, accommodating a chalcogen atom at an O-site of BaTiO3 is thermodynamically challenging owing to large differences in the atomic radii and electronegativities of oxygen and chalcogen atoms. In the present study we employ first-principles density functional theory calculations to examine the influence of Zr codoping on the structural, thermodynamic, opto-electronic properties and photocatalytic performance of X-doped (X = S, Se and Te) BaTiO3 systems. The atomic structure and energetic properties are computed using SCAN meta-GGA functional of density functional theory, while the electronic and optical properties are computed using the TB-mBJ meta-GGA potential functional. Within the valid limits of the atomic chemical potentials, we find that chalcogen doping in BaTiO3 lattice would be experimentally difficult despite a clear reduction in the electronic band gap of this system useful for application in visible light driven photocatalysis. In order to improve the synthesis feasibility of X-doped BaTiO3 under oxygen-rich as well as oxygen-poor chemical environments, we propose Zr as a codopant at a Ti-site in X-doped BaTiO3 which improves the thermodynamic stability and also retains the reduction in the electronic band gap of BaTiO3 caused by the presence of chalcogen atom. Our results suggest that Zr+X (X = S, Se and Te) codoped BaTiO3 offers great opportunities as a practical photocatalysts for hydrogen production through overall splitting of the water molecule.