We investigate transport on regular fracture networks that are characterized by heterogeneity in hydraulic conductivity. We discuss the impact of conductivity heterogeneity and mixing within fracture intersections on particle spreading. We show the emergence of non-Fickian transport due to the interplay between the network conductivity heterogeneity and the degree of mixing at nodes. Specifically, lack of mixing at fracture intersections leads to subdiffusive scaling of transverse spreading but has negligible impact on longitudinal spreading. An increase in network conductivity heterogeneity enhances both longitudinal and transverse spreading and leads to non-Fickian transport in longitudinal direction. Based on the observed Lagrangian velocity statistics, we develop an effective stochastic model that incorporates the interplay between Lagrangian velocity correlation and velocity distribution. The model is parameterized with a few physical parameters and is able to capture the full particle transition dynamics. © 2015 American Physical Society. ; PKK and RJ acknowledge the support of the US Department of Energy (grant DE-SC0003907), and a MISTI Global Seed Funds award. MD acknowledges the support of the European Research Council (ERC) through the project MHetScale (617511). TLB acknowledges the support of the INTERREG IV project CLIMAWAT. The data to reproduce the work can be obtained from the corresponding author ; Peer reviewed