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 ideal FPs are provided. The main contributions of this paper are the following: (1) We propose the use of the U-net neural network architecture for FP normalisation tasks; (2) we propose a modification for the distribution of weights in the U-net, called here the V-net model, which is more convenient for reconstruction tasks, and we conduct extensive experimental evidence in which the V-net produces high-quality results for FP filtering and normalisation. (3) We also propose two modifications of the V-net scheme, namely, a residual version called ResV-net and a fast operating version of the V-net, to evaluate the potential improvements when modify our proposal. We evaluate the performance of our methods 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.