Following the Paris agreement in 2015, the European Union (EU) set a carbon neutrality objective by 2050, and so did France. The French agricultural sector can contribute as a carbon sink through carbon storage in biomass and soil, in addition to reducing GHG emissions. The objective of this study is to quantitatively assess the additional storage potential and cost of a set of eight carbon-storing practices. The impacts of these agricultural practices on soil organic carbon storage and crop production are assessed at a very fine spatial scale, using crop and grassland models. The associated area base, GHG budget, and implementation costs are assessed and aggregated at the region level. The economic model BANCO uses this information to derive the marginal abatement cost curve for France and identify the combination of carbon storing practices that minimizes the total cost of achieving a given national net GHG mitigation target. We find that a substantial amount of carbon, 36.2 to 52.9 MtCO2e yr-1, can be stored in soil and biomass for reasonable carbon prices of 55 and 250 € tCO2e-1, respectively (corresponding to current and 2030 French carbon value for climate action), mainly by developing agroforestry and hedges, generalising cover crops, and introducing or extending temporary grasslands in crop sequences. This finding questions the 3–5 times lower target of 10 MtCO2e.yr-1 retained for the agricultural carbon sink by the French climate neutrality strategy. Overall, this would decrease total French GHG emissions by 9.2–13.8%, respectively (reference year 2019).