The fault–fracture system plays a crucial role in the migration, accumulation, and preservation of shale oil. However, weak geophysical response of these fractures and the ambiguity in picking faults and natural fractures make their identification and recognition challenging. To address these issues, this paper proposes a set of methods for predicting the distribution of fault–fracture systems based on graph neural networks. The method set consists of three parts: (1) a logging-based fracture identification method via graph pooling and global graph construction, which uses logging data sampling points to create small-scale graphs that simulate fracture distribution in the wellbore and integrates lithology, stratigraphy, and mechanical stratigraphy information into the global graph structure and fracture identification model through depth sequences, spatial distance calculations, and global graph convolution; (2) a method combining semantic segmentation with graph convolution, which adds fault graph structures and graph computation modules to the U-Net network to expand the receptive field and clarify segmentation boundaries of the model, and constructs a joint loss function to simultaneously train and optimize the fault segmentation and fault continuity analysis modules; (3) a fracture intensity prediction method combining fault damage zone graph construction with ensemble learning, which effectively integrates the controlling effect of faults on fractures into the inter-well fracture distribution prediction model through information transfer between vertices. The proposed method set was applied to the Fengcheng Formation in the Mabei area of the Junggar Basin, achieving fracture identification accuracy of 91.96% through conventional logging data, a fault detection accuracy of 97.38%, and a mean absolute error of tectonic fracture distribution prediction of 9.38%, representing a 22.47% improvement over existing technologies. Overall, the research findings provide a new approach for predicting the distribution of fault–fracture systems in shale oil reservoirs.