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European agro-food systems have negative impacts on the climate and the biodiversity, and unbalanced diets have harmful effects on health. The European Green Deal addresses these issues through a systemic approach to the food chain. Using an original partial equilibrium model, we show that substantially improving the climate, biodiversity, and nutrition performance of European agri-food systems requires jointly using the three main levers of the Green Deal, that is, 1) extensifying agricultural practices, 2) reducing food losses, and 3) shifting toward healthier average diets containing lower quantities of animal-based products. We identify four main tension points that require attention from public authorities and actors. They concern 1) the conditions for success of the agro-ecological transition of farming practices, 2) the impact of the Green Deal on European agri-food trade, 3) changes in consumers’ preferences and behaviours that would lead them to adopt more sustainable and healthier eating patterns, and 4) the challenge for the livestock sector in a context where such eating patterns imply a sharp reduction in the consumption and production of animal products.