Fractures and their connectivity are essential for fluid flow in low perme-ability formations. Abundant outcrops can only provide two-dimensional (2D) information, but subsurface fractures are three-dimensional (3D). The percola-tion status of 3D fracture networks and their 2D cross-section maps are rarely investigated simultaneously. In this work, we construct 3D fracture networks with their geometries characterized by different stochastic distributions. Then, we take cross-section maps to mimic real outcrops and label clusters to check the percolation status of 3D fracture networks and their 2D cross-section maps. The properties, reflecting the connectivity of two essential phases, are summarized and analyzed. We find that clustering effects impact local intersections significantly but have negligible impacts on fracture intensities of 3D fracture networks. The number of intersections per fracture is not a proper percolation parameter for complex 2D and 3D fracture networks. Fracture intensities are scale-dependent and usually decrease with increasing scales. The real fracture networks in the subsurface should be geometrically well-connected and pervasive if their outcrop maps are well connected. In particular, the fracture intensity of the real fracture network can be several times (at least 3.6 times) larger than the intensity at percolation. However, if outcrop maps are not well-connected, but their intensities are large enough (at least 0.43 times as large as the intensity at percolation), corresponding 3D fracture networks can also form a spanning cluster and show good connectivity with a high possibility.