Cohesive Zone Models with finite thickness are widely used for the fracture mechanical modeling of layers of material, e.g., adhesives. Within this approach, the whole layer is modeled as a Cohesive Zone. Moreover, computational homogenization techniques are crucial for the development of advanced engineering materials, which are often heterogeneous. Compared to the classical Finite Element Method (FEM), computationally more efficient solvers based on the Fast Fourier Transform (FFT) are expected to reduce the computational effort needed for the homogenization. Originated from an existing method for the computational homogenization of Cohesive Zones using FEM, a novel FFT-based homogenization scheme for Cohesive Zone Models was developed. Our implementation of the FFT solver uses the Barzilai-Borwein scheme and a non-local ductile damage model for the fracture behavior. Finally, the method is applied to the core material of HybrixTM metal sandwich plates, and the good agreement with experimental results in opening mode I is shown.