In 3D optical metrology, single-shot structured light profilometry techniques have inherent advantages over their multi-shot counterparts in terms of measurement speed, optical setup simplicity, and robustness to motion artifacts. In this paper, we present a new approach to extract height information from single deformed fringe patterns, based entirely on deep learning. By training a fully convolutional neural network on a large set of simulated height maps with corresponding deformed fringe patterns, we demonstrate the ability of the network to obtain full-field height information from previously unseen fringe patterns with high accuracy. As an added benefit, intermediate data processing steps such as background masking, noise reduction and phase unwrapping that are otherwise required in classic demodulation strategies, can be learned directly by the network as part of its mapping function.