Effects of Pauli paramagnetism on thermodynamic quantities in a vortex state, such as the specific heat C and magnetization M, are studied using the quasiclassical Eilenberger formalism. We demonstrate that with an increase of paramagnetic depairing effect, the sigh of the curvature of the field dependence of C changes from negative to positive, and that the Maki parameter kappa(2) becomes an increasing function of temperature. Our results provide a natural explanation for the unusual field dependence of C seen in CeCoIn5 in terms of the paramagnetic effect.