The accurate split of large areas of land into discrete fields is a crucial step for several agriculture-related remote sensing pipelines. This work aims to fully automate this tedious and resource-demanding process using a state-of-the-art deep learning algorithm with only a single Sentinel-2 image as input. The Mask R-CNN, which has forged its success upon instance segmentation for objects from everyday life, is adapted for the field boundary detection problem. Such model automatically generates closed geometries without any heavy post-processing. When tested with satellite imagery from Denmark, this tailored model correctly predicts field boundaries with an overall accuracy of 0.79. Besides, it demonstrates a robust knowledge generalisation with positive results over different geographies, as it gets an overall accuracy of 0.71 when used over areas in France.