Many studies have assessed the potential of agricultural practices to sequester carbon (C). A comprehensive evaluation of impacts of agricultural practices requires not only considering C storage but also direct and indirect emissions of greenhouse gases (GHG) and their side effects (e.g., on the water cycle or agricultural production). We used a high‐resolution modeling approach with the Simulateur mulTIdisciplinaire pour les Cultures Standard soil‐crop model to quantify soil organic C (SOC) storage potential, GHG balance, biomass production and nitrogen‐ and water‐related impacts for all arable land in France for current cropping systems (baseline scenario) and three mitigation scenarios: (i) spatial and temporal expansion of cover crops, (ii) spatial insertion and temporal extension of temporary grasslands (two sub‐scenarios) and (iii) improved recycling of organic resources as fertilizer. In the baseline scenario, SOC decreased slightly over 30 years in crop‐only rotations but increased significantly in crop/temporary grassland rotations. Results highlighted a strong trade‐off between the storage rate per unit area (kg C ha−1 year−1) of mitigation scenarios and the areas to which they could be applied. As a result, while the most promising scenario at the field scale was the insertion of temporary grassland (+466 kg C ha−1 year−1 stored to a depth of 0.3 m compared to the baseline, on 0.68 Mha), at the national scale, it was by far the expansion of cover crops (+131 kg C ha−1 year−1, on 17.62 Mha). Side effects on crop production, water irrigation and nitrogen emissions varied greatly depending on the scenario and production situation. At the national scale, combining the three mitigation scenarios could mitigate GHG emissions of current cropping systems by 54% (−11.2 from the current 20.5 Mt CO2e year−1), but the remaining emissions would still lie far from the objective of C‐neutral agriculture.