Floods resulting from high-intensity rainfall events are known to be difficult to simulate. The catchment response to such events is very heterogeneous due to complex combinations of hydrological processes at fine temporal and spatial scales. The goal of this study is to find a way to inform the structure of a hydrological model on the variability in catchment response to rainfall events. To that end, rainfall intensity was used as a proxy for the activation of fast heterogeneous runoff processes. We developed three hypotheses that increase the versatility of a hydrological model by modifying the volume and temporal distribution of effective rainfall when high-intensity rainfall events occur. These modifications were implemented within the GR5H lumped rainfall–runoff model. The different model versions were run on 229 French catchments where 10 652 flood events were selected. Model performance was assessed considering five groups of catchments, and model performance was also evaluated based on three event characteristics. Results showed that introducing a dynamic dependency of fluxes to rainfall intensities at the hourly time step helps to improve the simulation of floods, especially on Mediterranean catchment areas. Generic values of the additional parameters are proposed to limit the increase in calibration complexity.