SARS-Cov-2 virus has spread over the world creating one of the fastest pandemics ever. The absence of immunity, asymptomatic transmission, and the relatively high level of virulence of the COVID-19 infection it causes led to a massive flow of patients in intensive care units (ICU). This unprecedented situation calls for rapid and accurate mathematical models to best inform public health policies. We develop an original parsimonious model that accounts for the effect of the age of infection on the natural history of the disease. Analysing the ongoing COVID-19 in France, we estimate the value of the key epidemiological parameters, such as the basic reproduction number (R0), and the efficiency of the national control strategy. We then use our deterministic model to explore several scenarios posterior to lock-down lifting and compare the efficiency of non pharmaceutical interventions (NPI) described in the literature.