Journal article: We are developing a matching model that reproduces the impact of the sanitary restrictions induced by the Covid-19 crisis on French unemployment, taking into account its heterogenous impacts between various educational levels. We identify the size of the restrictions on sales for each labor market segment and the different use of short-time working program. Our results are obtained thanks to an original matching model integrating (i) time-varying microeconomic risks, (ii) and congestion externalities making unit costs of vacancy posting varying. Afterwards, (i) we evaluate the impact of the short-time working program on unemployment rates by diploma, (ii) we compare different scenarios of the lockdown (short but strict vs long but flexible) and (iii) we forecast the impact of a similar lockdown of March 2020 at the end of March 2021.