The increasing consumption of seafood products raises concerns over the sustainability of marine ecosystems. We examine the role of seafood demand 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 demand features making it possible to balance biodiversity conservation with viable profits. We exemplify the analytical results with the coastal fishery and the seafood system in French Guiana.