Multichannel methods have attracted much attention in color image denoising. These are image denoising methods that combine the low-rankness of a matrix with the nonlocal self-similarity of a natural image. The methods apply to color images with noise of different intensities in each color channel. Denoising methods based on the low-rankness of tensors, and extensions of matrices, have also attracted attention in recent years. Many tensor-based methods have been proposed as extensions of matrix-based methods and have achieved higher denoising performance than matrix-based methods. Tensor-based methods perform denoising using an approximate function of the tensor rank. However, unlike multichannel methods, tensor-based methods do not assume different noise intensities for each channel. On the other hand, the tensor nuclear norm minus Frobenius norm (TNNFN) has been proposed in the domain of traffic data completion. The TNNFN is one of the tensor rank approximation functions and is known to have high performance in traffic data completion, but it has not been applied to image restoration. In this paper, we propose MC-TNNFN as a tensor-based multichannel method. It is a TNNFN-based multichannel method that uses TNNFN to remove noise from a tensor constructed from similar patches and then estimates the original image. Experimental results using natural images show that the proposed method outperforms existing methods objectively and subjectively.