In this paper we analyze some important characteristics of the spatial Wigner function of entangled photon pairs. We show that the Wigner description of quantum states that live in the infinite-dimensional spacemomentum degree of freedom proves to be particularly useful. We propose an experimental configuration that can be used to retrieve the Wigner function of paired photons entangled in the spatial degree of freedom. In particular, it allows the full characterization of the paired photons emitted from a spontaneous parametric down-conversion source. ; Postprint (published version)