Using an agricultural supply model developed for the European Union, we assess the production potential to satisfy two objectives, one related to food calories, the other to biofuels replacing fossil fuels. For energy-related production, we distinguish between gasoline and diesel substitutes. The production set is provided for France, by varying the thresholds for food calorie and bioenergy simultaneously. We find that France shows a large potential of biomass resources that allows a great margin for action where food and energy security could be compatible and associated economic viability and environmental protection. If the feasible set reveals a high production potential in the both food and energy dimensions, the implicit high prices associated with the two constraints show that this potential could only be achieved at the cost of substantial structural and spatial changes of the agricultural production system. We show in particular the emerging tension on animal production and even more on animal feed, and we find that food and bioenergy production targets jointly induce significant greenhouse gases emissions reductions.