We studied in detail the in-plane magnetic properties of heterostructures based on a ferroelectric BaTiO₃ overlayer deposited on a ferromagnetic La_2/3Sr_1/3MnO₃ film grown epitaxially on pseudocubic (001)-oriented SrTiO₃, (LaAlO₃)_0.3(Sr₂TaAlO₆)_0.7 and LaAlO₃ substrates. In this configuration, the combination of both functional perovskites constitutes an artificial multiferroic system with potential applications in spintronic devices based on the magnetoelectric effect. La_2/3Sr_1/3MnO₃ single layers and BaTiO₃/La_2/3Sr_1/3MnO₃ bilayers using the pulsed-laser deposition technique. We analyzed the films structurally through X-ray reciprocal space maps and high-angle annular dark field microscopy, and magnetically via thermal demagnetization curves and in-plane magnetization versus applied magnetic field loops at room temperature. Our results indicate that the BaTiO₃ layer induces an additional strain in the La_2/3Sr_1/3MnO₃ layers close to their common interface. The presence of BaTiO₃ on the surface of tensile-strained La_2/3Sr_1/3MnO₃ films transforms the in-plane biaxial magnetic anisotropy present in the single layer into an in-plane uniaxial magnetic anisotropy. Our experimental evidence suggests that this change in the magnetic anisotropy only occurs in tensile-strained La_2/3Sr_1/3MnO₃ film and is favored by an additional strain on the La_2/3Sr_1/3MnO₃ layer promoted by the BaTiO₃ film. These findings reveal an additional mechanism that alters the magnetic behavior of the ferromagnetic layer, and consequently, deserves further in-depth research to determine how it can modify the magnetoelectric coupling of this hybrid multiferroic system.