In this paper we provide a FFT algorithm to compute the effective permeability of doubly porous solids constituted of two populations of pores which are different in size. The paper focuses on the resolution of the fluid flow at the intermediate scale, that of the macropores, that requires the resolution of the coupled Darcy/Stokes problem. The permeability associated with the first population of cavities is assumed to be known. A two-field FFT based iterative scheme is derived to compute the solution of the Darcy/Stokes problem. The principle is to reformulate the problem by considering a unique Brinkman equation with different coefficients for the Darcy and the Stokes regions. As a first application, we determine the macroscopic permeability of a porous solid containing circular macropores. The results are compared to analytic expressions and simplified modeling which use an equivalent Darcy medium in place of the macropores. Next, we apply the FFT method to a bi-porous polymer. The computations are performed on 2D and 3D cells extracted from X-ray computed microtomography.