European farming systems (FSs) are currently dependent on oil to transport feed and to synthesise fertilisers. Disturbances, such as reaching the global peak oil by 2030, can therefore result in supply shortages. It is necessary to investigate the robustness of European FSs, i.e., their capacity to maintain agricultural production with their current crop–grassland–livestock composition. The aims were to (1) assess the robustness of French FSs to a joint decline in input supplies and (2) explore the links between robustness and crop–grassland–livestock compositions. We simulated a progressive 30-year decline of synthetic fertiliser use and feed imports with a time-dynamic FS nitrogen flow model. We then clustered the FSs according to their robustness levels and examined at the national scale the relationships between these clusters and compositional indicators. French FSs maintained agricultural production for a median of 9 years before experiencing a 68% drop in agricultural production after 30 years. The most-specialised FSs (vineyards, intensive monogastrics and field crops) were the least robust in the short term (4–7 years), as they were the most dependent on inputs to meet their needs; however, they were the most robust in the long term (60% reduction), except for field crops (∼75% reduction). Mixed FSs were the most robust in the short term (8–19 years); however, their robustness levels depended on the degree of crop–livestock integration. Changes in compositions that decrease supply dependency, such as a reduction in feed–food competition, should be implemented as soon as possible to increase the FSs resilience.