4D occupancy forecasting is one of the important techniques for autonomous driving, which can avoid potential risk in the complex traffic scenes. Scene flow is a crucial element to describe 4D occupancy map tendency. However, an accurate scene flow is difficult to predict in the real scene. In this paper, we find that BEV scene flow can approximately represent 3D scene flow in most traffic scenes. And coarse BEV scene flow is easy to generate. Under this thought, we propose 4D occupancy forecasting method FSF-Net based on coarse BEV scene flow. At first, we develop a general occupancy forecasting architecture based on coarse BEV scene flow. Then, to further enhance 4D occupancy feature representation ability, we propose a vector quantized based Mamba (VQ-Mamba) network to mine spatial-temporal structural scene feature. After that, to effectively fuse coarse occupancy maps forecasted from BEV scene flow and latent features, we design a U-Net based quality fusion (UQF) network to generate the fine-grained forecasting result. Extensive experiments are conducted on public Occ3D dataset. FSF-Net has achieved IoU and mIoU 9.56% and 10.87% higher than state-of-the-art method. Hence, we believe that proposed FSF-Net benefits to the safety of autonomous driving.