In this paper, we use the replica trick in order to compute the effective permittivity of a medium where the local permittivity is a random binary variable. A Gaussian variational treatment leads us to self-consistent equations which are solved and yield a replica diagonal solution (no replica symmetry breaking). We obtain an effective-medium formula previously derived by a cumulant expansion. This formula is satisfactory from many points of views (Hashin and Shtrikman bounds, low density expansion, etc) showing that the replica method does not violate some basic principles