Assessment of the cumulative incidence of SARS-CoV-2 infections is critical for monitoring the course and extent of the COVID-19 epidemic. Here, we report estimated seroprevalence in the French population and the proportion of infected individuals who developed neutralising antibodies at three points throughout the first epidemic wave. Testing 11,000 residual specimens for anti-SARS-CoV-2 IgG and neutralising antibodies, we find nationwide seroprevalence of 0.41% (95% CI: 0.05-0.88) mid-March, 4.14% (95% CI: 3.31-4.99) mid-April and 4.93% (95% CI: 4.02-5.89) mid-May 2020. Approximately 70% of seropositive individuals have detectable neutralising antibodies. Infection fatality rate is 0.84% (95% CI: 0.70-1.03) and increases exponentially with age. These results confirm that the nationwide lockdown substantially curbed transmission and that the vast majority of the French population remained susceptible to SARS-CoV-2 in May 2020. Our study shows the progression of the first epidemic wave and provides a framework to inform the ongoing public health response as viral transmission continues globally.