The role of aquifers in the seasonal and multiyear dynamics of streamflow is undisputed: in many temperate catchments, aquifers store water during the wet periods and release it all year long, making a major contribution to low flows. The complexity of groundwater modelling has long prevented surface hydrological modellers from including groundwater level data, especially in lumped conceptual rainfall–runoff models. In this article, we investigate whether using groundwater level data in the daily GR6J model, through a composite calibration framework, can improve the performance of streamflow simulation. We tested the new calibration process on 107 French catchments. Our results show that these additional data are superfluous if we look only at model performance for streamflow simulation. However, parameter stability is improved, and the model shows a surprising ability to simulate groundwater levels with a satisfying level of performance in a wide variety of hydrogeological and hydroclimatic contexts. Finally, we make several recommendations regarding the model calibration process to be used according to the hydrogeological context of the modelled catchment.