A wireline NMR (Nuclear Magnetic Resonance) logging tool has recently been deployed in the Dogger geothermal aquifer of the Paris Basin to provide a continuous permeability estimation throughout the reservoir. The complex pore structure of heterogeneous carbonate systems means that careful consideration must be given to standard permeability prediction. A laboratory study was performed on cores from a geothermal well at Bobigny, north of Paris. Petrographic and petrophysical analyses of thin sections, water permeability and laboratory NMR relaxation time T2 were conducted on 72 samples. A classification was established using four main facies and the impact of microporosity and micritization on flow properties was investigated. The range of permeability is wide [0.05–1000 mD] and the evaluation addresses different relationships between permeability and a combination of porosity and T2 distributions. Since the latter distributions can provide an estimation of the pore size distributions and in particular the fraction of microporosity within the total porosity, several possibilities arise for better constraining the permeability relationship. For one facies, permeability is nearly independent of porosity over a porosity range of [0.12–0.22], illustrating the well-known difficulty of predicting permeability in carbonate lithologies. The best permeability prediction is obtained when considering only macroporosity instead of total porosity in a classical power law.