The realism of Discrete Fracture Network (DFN) models, beyond the bulk statistical properties, relies on the spatial organization of fractures, which is not issued by classical stochastic DFN models. This can be improved by injecting prior information in DFN from a better knowledge of the geological fracturing processes. We first develop a model using simple kinematic rules for mimicking the growth of fractures from nucleation to stop, in order to evaluate the consequences of realistic DFN on the network connectivity and flow structure. The model generates fracture networks with power-law scaling distributions and a percentage of T-intersections that are consistent with field observations. Nevertheless, a larger complexity relying on the spatial variability of natural fractures positions cannot be explained by the random nucleation process. We propose to introduce a stress-driven nucleation in the timewise process of this kinematic model to study the correlations between nucleation, growth and existing fracture patterns. The method uses the stress field generated by existing fractures and remote stress as an input for a Monte-Carlo sampling of nuclei centers at each time step. Networks so generated are found to have fractal correlations over a large range of scales, with a dimension that varies with time and with the function that relates the nucleation probability to stress. A sensibility analysis of input parameters has been performed in 3D to quantify the influence of fractures and remote stress field orientations.