Digital image watermarking has justified its suitability for copyright protection and copy control of digital images. In the past years, various watermarking schemes were proposed to enhance the fidelity and the robustness of watermarked images against different types of attacks such as additive noise, filtering, and geometric attacks. It is highly important to guarantee a sufficient level of robustness of watermarked images against such type of attacks. Recently, Deep learning and neural networks achieved noticeable development and improvement, especially in image processing, segmentation, and classification. Therefore, in this paper, we studied the effect of a Fully Convolutional Neural Network (FCNN), as a denoising attack, on watermarked images. This deep architecture improves the training process and denoising performance, through which the encoder-decoder remove the noise while preserving the detailed structure of the image. FCNNDA outperforms the other types of attacks because it destroys the watermarks while preserving a good quality of the attacked images. Spread Transform Dither Modulation (STDM) and Spread Spectrum (SS) are used as watermarking schemes to embed the watermarks in the images using several scenarios. This evaluation shows that such type of denoising attack preserves the image quality while breaking the robustness of all evaluated watermarked schemes. It could also be considered a deleterious attack.