International research and development organizations have acknowledged that localized agrifood systems, particularly geographical indications (GIs), are a lever for evolving towards sustainable agriculture. Such a premise is neither spontaneous nor systematic. Research and development organizations show their limit in proposing approaches to overcome this raised issue: The performance-based approach of sustainability, associated with a strict economical understanding of activities, is at stake. We propose the introduction of a values-based approach to the understanding of localized activities and their contribution to sustainability. We base our demonstration on the study of the relationships between stakeholders within GIs on a day-to-day basis: Corsica and Western Pyrenees (WP) are regions where traditional cheeses (respectively GI Brocciu and GI Ossau-Iraty) are produced with ewe milk. We build a typology of relationships between farmers providing the milk and dairies, based on the theory of worlds of worth (from industrial to artisanal). We cross-reference it with values given to milk and cheese. Despite the framing role of GIs, milk is mainly valued according to industrial criteria of quantity and sound farming practices have no weightage. However, artisanal and civic initiatives have emerged using raw milk and fostering more sustainable practices, notably based on organic farming. Though those initiatives are currently marginal, they might be promising seeds of change.