We propose a new framework for processing Fringe Patterns (FP). Our novel approach builds upon the hypothesis that the denoising and normalisation of FPs can be learned by a deep neural network if enough pairs of corrupted and cleaned FPs are provided. Although similar proposals have been reported in the literature, we propose an improvement of a well-known deep neural network architecture, which produces high-quality results in terms of stability and repeatability. We test the performance of our method in various scenarios: FPs corrupted with different degrees of noise, and corrupted with different noise distributions. We compare our methodology versus other state-of-the-art methods. The experimental results (on both synthetic and real data) demonstrate the capabilities and potential of this new paradigm for processing interferograms. We expect our work would motivate more sophisticated developments in this direction.