A numerical study reports that the zero-field skyrmions in FeGe thin films are stabilized when a FeGe layer is exchange coupled to a single-domain Ni layer, which has been magnetized perpendicularly. Due to the small thickness, an easy-plane anisotropy in the FeGe layer is taken into account, and the skyrmion-crystal state is favored to appear for low anisotropies and intermediate FeGe/Ni interlayer exchange couplings, and finally transformed from a labyrinth-like and into an out-of-plane uniform state for the large couplings or into an in-plane state for the high anisotropies. Furthermore, the maximum skyrmion charge number is bigger for the periodic and fixed boundary conditions with an out-of-plane magnetization; on the contrary, the Bloch-type skyrmions can be frozen and stabilized for the larger couplings on the fixed boundary with an in-plane magnetization, similar to the experimental results of the magnetic-field-induced skyrmions. Finally, the skyrmion charge number and diameter both decrease if the nonmagnetic defects exist, and the skyrmion centers are prone to being captured by defect sites. This work evidences that the ensembles of homochiral skyrmions stabilized in the multilayers fabricated by well-established technologies present a roadmap to design new classes of the materials that can host skyrmions.