In the framework of density functional theory (DFT) using Tran--Blaha modified Becke--Johnson exchange potential approximation (TB-mBJ), the structural, electronic, optical and mechanical, characteristics of cubic fluoroperovskites TiXF3 (X = Zn, Cu) are investigated. The structural properties, including equilibrium lattice constant, the bulk modulus (B) and its pressure derivative (B') are studied. Both the compounds are found to be stable structurally in its cubic form. The elastic characteristics, i-e anisotropy factor (A), Poisson's ratio (v), elastic constants, Young's modulus (E), and shear modulus (G) are investigated. The values of v and B/G ratio indicates that TiZnF3 and TiCuF3 compounds are ductile and brittle in nature respectively and exhibit anisotropy. In addition, these materials are resistant to plastic deformation due to the high G value. The electronic band structure, density of states (DOS) verifies the semiconducting and metallic nature with energy band gap of 5.4 and 0 eV of TiXF3 (X = Zn, Cu) compounds respectively. Ionic bonding character is found in both TiXF3 (X = Zn, Cu) compounds. Calculations of the optical spectrum like energy loss function L(ω), optical conductivity σ(ω), absorption coefficient α(ω), reflectivity R(ω), refractive index n(ω), and extinction coefficient k(ω) are carried out for the energy range 0 eV-13.5 eV. It is reported that n( ω), k( ω), and α( ω) exhibit identical characteristics as ε1( ω) and ε2( ω) and σ(ω) respectively. The thermoelectric properties study shows the very high value of ZT for TiCuF3. Since the above properties for these compounds are computed for the first time, therefore, no theoretical or experimental data is available for the comparison. [ABSTRACT FROM AUTHOR]