We proposed a low complexity OFDM-Guided deep joint source-channel coding (DJSCC) model for wireless multipath fading channels using fine-tuned tensor train (TT) decomposition. Using the optimal rank of the TT decomposition, we fine-tuned the small number of intermediate channels that lead to incomplete feature extraction after the TT decomposition. The original OFDM-guided DJSCC model is first hierarchically TT decomposition, followed by fine-tuning the size of the intermediate convolution layers to improve the performance. From the experimental results, we found that the smaller the signal-to-noise ratio (SNR) value, the smaller the loss of peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM) performance. The best compressed model using TT decomposition with fine-tuning loses about 4% of PSNR performance and 2% of the SSIM performance, with a compression ratio of about 17% and a reduction of the number of parameters by 6 times of the original OFDM-guided DJSCC model.