In this paper, a new classification approach of breast cancer based on Fully Convolutional Networks (FCNs) and Beta Wavelet Autoencoder (BWAE) is presented. FCN, as a powerful image segmentation model, is used to extract the relevant information from mammography images. It will identify the relevant zones to model while WAE is used to model the extracted information for these zones. In fact, WAE has proven its superiority to the majority of the features extraction approaches. The fusion of these two techniques have improved the feature extraction phase and this by keeping and modeling only the relevant and useful features for the identification and description of breast masses. The experimental results showed the effectiveness of our proposed method which has given very encouraging results in comparison with the states of the art approaches on the same mammographic image base. A precision rate of 94% for benign and 93% for malignant was achieved with a recall rate of 92% for benign and 95% for malignant. For the normal case, we were able to reach a rate of 100%.