In the present work, we provide results from specific heat, magnetic susceptibility, dielectric constant, ac conductivity, and electrical polarization measurements performed on the lacunar spinel GaV4Se8. With decreasing temperature, we observe a transition from the paraelectric and paramagnetic cubic state into a polar, probably ferroelectric state at 42 K followed by magnetic ordering at 18 K. The polar transition is likely driven by the Jahn-Teller effect due to the degeneracy of the V4 cluster orbitals. The excess polarization arising in the magnetic phase indicates considerable magnetoelectric coupling. Overall, the behavior of GaV4Se8 in many respects is similar to that of the skyrmion host GaV4S8, exhibiting a complex interplay of orbital, spin, lattice, and polar degrees of freedom. However, its dielectric behavior at the polar transition markedly differs from that of the Jahn-Teller-driven ferroelectric GeV4S8, which can be ascribed to the dissimilar electronic structure of the Ge compound.