European Union (EU) policies have been evolving beyond the protection of consumers through food safety protocols to the promotion of healthy and sustainable diets. The European Commission’s Farm to Fork Strategy—the most recent step in this evolution—addresses challenges facing European agriculture and proposes measures for creating a more resilient as well as sustainable food system, which includes a plan for product labelling. The effort to improve information conveyed to consumers through product labelling is a long-standing and ongoing phenomenon, and different front-of-pack voluntary labels presently co-exist across EU Member States. One objective of the Farm to Fork Strategy is to harmonize them; a second objective, no less important, is to add ‘sustainability’ as an additional quality to be certified through labels. Yet, adopting some of the current models of voluntary front-of-pack labels—in order to better promote both dietary health and sustainability—might conflict with already-established measures implemented by the Common Agricultural Policies, such as Geographical Indication protection for agri-food products. Furthermore, influencing consumers’ behaviour through labelling should not be regarded as equivalent to ‘empowering’ consumers in terms of nutrition and sustainable choices. Labelling needs to be complemented by higher levels of policy interventions—incentives/disincentives or even policies that limit or restrict choices—in order to rebalance power in the food supply chain and to induce a change in the complex social practices of food consumption. This paper examines the Farm to Fork Strategy through an analysis of EU policy documents, existing literature, and the discussion of a case study—with particular attention paid to the role of labels in promoting healthy and sustainable diets as well as the possibility of new sustainability criteria for products certified with Geographic Indications.