The temporal and spatial scale of interest of CO2 storage studies lies in between reservoir and basin models. While reservoir modelling software is best fitted to address some of the multiphysics issues related to the behaviour of CO2 once injected into the subsurface (adsorption, dissolution, near injection wellbore mechanics and temperature, and, in some cases, fluid rock interaction) within a human timescale, basin modelling tools handle better the full basin volume and time-scale heterogeneities that impact the storage potential and risk associated with CO2 injection. This study takes a basin modelling approach to provide an assessment of the influence of geological evolution on CO2 storage capacity, both at the reservoir level, by helping to estimate the amount of CO2 that can be stored in its connected porosity, and at the cap-rock level, by assessing the seal integrity. Our basin model also captures the evolution of the pressure plume induced by the CO2 injection, taking into account the pressure and temperature fields, aquifer connectivity and permeability, and seal integrity, on a much shorter timescale than is usually considered by such a model. The results show the impact of basin evolution on aquifer properties and consequently on the dissipation of the induced pressure plume. They also highlight the large-scale influence of the CO2 on the pressure field both vertically along the stratigraphic column, when the pressure plume reaches shallower aquifers through unconformities, and horizontally, when good aquifer injectivity and connectivity allows the pressure plume to dissipate widely.