Video compression relies heavily on exploiting the temporal redundancy between video frames, which is usually achieved by estimating and using the motion information. The motion information is represented as optical flows in most of the existing deep video compression networks. Indeed, these networks often adopt pre-trained optical flow estimation networks for motion estimation. The optical flows, however, may be less suitable for video compression due to the following two factors. First, the optical flow estimation networks were trained to perform inter-frame prediction as accurately as possible, but the optical flows themselves may cost too many bits to encode. Second, the optical flow estimation networks were trained on synthetic data, and may not generalize well enough to real-world videos. We address the twofold limitations by enhancing the optical flows in two stages: offline and online. In the offline stage, we fine-tune a trained optical flow estimation network with the motion information provided by a traditional (non-deep) video compression scheme, e.g. H.266/VVC, as we believe the motion information of H.266/VVC achieves a better rate-distortion trade-off. In the online stage, we further optimize the latent features of the optical flows with a gradient descent-based algorithm for the video to be compressed, so as to enhance the adaptivity of the optical flows. We conduct experiments on two state-of-the-art deep video compression schemes, DCVC and DCVC-DC. Experimental results demonstrate that the proposed offline and online enhancement together achieves on average 13.4% bitrate saving for DCVC and 4.1% bitrate saving for DCVC-DC on the tested videos, without increasing the model or computational complexity of the decoder side.