Public authorities and consumers increasingly support food value chains that are more environmentally friendly. However, these value chains are faced with technical, economic and institutional limitations, calling into question their long-term viability. Based on two case studies of alternative food chains in France, namely einkorn (Triticum monococcum) in Haute Provence and organic rice in the Camargue, we evaluated their capacity to remain both viable and environmentally, economically and socially sustainable. After assessing the traditional economic, social and environmental performance of their sustainability, we performed a network analysis to determine the survivability of the systems. The combined use of the traditional pillars of sustainability and the network analysis forms what we term the systemic sustainability. Results suggest that the einkorn value chain is characterised by a high degree of centrality represented by a producers' association, although the systemic sustainability of the chain is reduced by its dependence on a leading processor. As for the organic rice value chain, centralised power is exerted by three companies embedded in a strong network of actors characterised by diversified connections. The paper concludes by highlighting the potential interest of conducting a network analysis to better determine the sustainability of food value chains.