Image logs and the continuous coring of 8 geothermal wells in the Central Upper Rhine Graben (URG) are used for the structural characterization of 3 geothermal reservoirs at Soultz-sous-Forêts, Rittershoffen and Illkirch (France). The naturally permeable fracture zones (FZs) of the hard rocks are the targets of these wells. Subvertical natural fracture networks are striking NNW-SSE to N-S in the granite (inherited from the late-Variscan orogeny) and N-S/NNE-SSW in the sediments (mainly inherited from the Cenozoic era). The permeable fractures in the granite are subparallel to the main striking values. The fracture densities and thicknesses are the greatest in the first 500-1000 m of the granite. The fracture thickness surely reflects the intensity of the paleocirculations. The fracture distribution is governed by power laws and negative exponential laws. However, there is no simple relationship between those fracture properties and the present-day fracture permeability. The permeability is related to multiscale fracture networks channelling the fluids. Large-scale fractures within normal fault zones could be a more promising target than wide networks of distributed small-scale fractures affecting the whole granitic batholith. The geometry between the well trajectory and the fracture network, impacts also significantly the resulting permeability.