The SARS-CoV-2 virus has spread world-wide since December 2019, killing more than 2.9 million of people. We have adapted a statistical model from the SIR epidemiological models to predict the spread of SARS-CoV-2 in France. Our model is based on several parameters and assumed a 4.2% seroprevalence in Occitania after the first lockdown. The recent use of serological tests to measure the effective seroprevalence of SARS-CoV-2 in the population of Occitania has led to a seroprevalence around 2.4%. This implies to review the parameters of our model to conclude at a lower than expected virus transmission rate, which may be due to infectivity varying with the patient's symptoms or to a constraint due to an uneven population geographical distribution.