Copper (Cu) isotope compositions in bivalve mollusks used in marine-monitoring networks is a promising tool to monitor anthropogenic Cu contamination in coastal and marine ecosystems. To test this new biomonitoring tool, we investigated Cu isotope variations of two bivalves—the oyster Crassostrea gigas and the mussel Mytilus edulis—over 10 years (2009–2018) in a French coastal site contaminated by diffuse Cu anthropogenic sources. Each species displayed temporal concentration profiles consistent with their bioaccumulation mechanisms, that is, the Cu-regulating mussels with almost constant Cu concentrations and the Cu-hyperaccumulating oysters with variable concentrations that track Cu bioavailability trends at the sampling site. The temporal isotope profiles were analogous for both bivalve species, and an overall shift toward positive δ65Cu values with the increase of Cu bioavailabilities was associated with anthropogenic Cu inputs. Interestingly, mussels showed wider amplitudes in the isotope variations than oysters, suggesting that each species incorporates Cu isotopes in their tissues at different rates, depending on their bioaccumulation mechanisms and physiological features. This study is the first to demonstrate the potential of Cu isotopes in bivalves to infer Cu bioavailability changes related to anthropogenic inputs of this metal into the marine environment.