Tensor ring (TR) decomposition has demonstrated remarkable capability in capturing low-rank tensor structures, achieving significant success in color image completion tasks. However, relying solely on the tensor low-rank prior cannot fully capture the details of a color image. Thus, traditional model-driven TR decomposition models often fail to recover satisfactory local detail. A natural idea is to introduce a deep neural network with end-to-end training to improve the detail quality of image reconstruction. Thus, we proposed a novel hybrid model that integrates model-driven TR decomposition with data-driven deep learning regularization. The proposed framework introduces an energy functional regularization term based on the FFDNET architecture, which enhances the robustness of rank selection while preserving global low-rank and local details. In particular, we assumed that the unfolding matrices of the TR factors exhibited low-rank properties. Thus, nuclear-norm regularization constraints were incorporated on the TR factors to enhance their global low-rank characteristics. Additionally, a deep prior regularization term derived from the FFDNET network was introduced to preserve the local details of the target tensor. We further developed an efficient alternating direction method for the multiplier algorithm to address the associated optimization problem. Extensive experiments on color images have demonstrated that the proposed method outperforms denoising approaches, yielding satisfactory results. The code for implementing the proposed method is available at https://github.com/110500617/TRDD.