The Amazonian moist forest, which covers most of French Guiana, is one of the core habitats for the lowland tapir Tapirus terrestris. Tapirs are hunted in French Guiana, although a law introduced in 2011 restricts hunting to one animal per person per hunting trip. We carried out camera-trap surveys in the Nouragues Nature Reserve for 4 years, with the goal of estimating tapir densities in undisturbed conditions and determining sustainable harvest levels for tapirs in French Guiana. We analysed our data with a Bayesian spatially explicit capture–recapture model, with parameter sharing across surveys to improve estimates, and used the model to calculate derived parameters such as maximum sustainable harvest levels. Density estimates for all four surveys were similar and the model indicated a difference in encounter rates for the two camera models used but no difference in encounter rates or home range sizes for males and females or between years. Based on the calculated density of 0.32 tapir km−2 we estimated sustainable harvest levels at 0.009 tapir km−2. Comparing this value to hunting surveys from 11 sites between 1999 and 2006, we found that hunting levels were unsustainable in at least seven villages. We conclude that even the new restrictive hunting law will not prevent overhunting of tapirs in certain areas and thus stronger regulations are needed. However, because of the remoteness of tapir habitat in many parts of French Guiana tapirs are not immediately threatened in the country as a whole.