Copper–semicarbazone ligands have been extensively investigated for several medicinal applications. In this contribution, a novel copper(II) complex with a pyridoxal–semicarbazone ligand, [Cu(PLSC)Cl(H2O)](NO3)(H2O), was synthesized and characterized by X-ray crystallography, elemental analysis, UV-VIS, and FTIR spectroscopies. The stabilization interactions within the structure were assessed using the Hirshfeld surface analysis. The crystallographic structure was optimized at the B3LYP/6-311++G(d,p)(H,C,N,O)/LanL2DZ(Cu) level of theory. A comparison between the experimental and theoretical bond lengths and angles was undertaken to verify the applicability of the selected level of theory. The obtained high correlation coefficients and low mean absolute errors confirmed that the optimized structure is suitable for further investigating the interactions between donor atoms and copper, along with the interactions between species in a neutral complex, using the Quantum Theory of Atoms in Molecules approach. The electrostatic potential surface map was used to reveal distinct charge distributions. The experimental and calculated FTIR spectra were compared, and the most prominent bands were assigned. The interactions with human serum albumin (HSA) were assessed by spectrofluorometric titration. The spontaneity of the process was proven, and the thermodynamic parameters of binding were calculated. Molecular docking analysis identified the most probable binding site, providing additional insight into the nature of the interactions.