The increasing consumption of seafood products raises concerns over the sustainability of marine ecosystems. We examine the role of consumer preferences on seafood demand and consequently on the sustainability of fisheries. Our analysis relies on a bio-economic model combining a demand derived from a CES utility depending on different fish species, a mixed fishery supply based on the Schaefer production function, a market equilibrium and a multispecies resource-based dynamics. Using both a steady-state approach and bio-economic viability goals, we identify analytical conditions on consumer preferences making it possible to balance biodiversity conservation with viable profits. We derive policy recommendations in terms of eco-labels for the sustainability of fisheries and the underlying seafood system. We exemplify the analytical results with the coastal fishery in French Guiana.