Many European countries have responded to the COVID-19 pandemic by implementing nationwide protection measures and lockdowns1. However, the epidemic could rebound when such measures are relaxed, possibly leading to a requirement for a second or more, repeated lockdowns2. Here, we present results of a stochastic agent-based microsimulation model of the COVID-19 epidemic in France. We examined the potential impact of post-lockdown measures, including physical distancing, mask-wearing and shielding individuals who are the most vulnerable to severe COVID-19 infection, on cumulative disease incidence and mortality, and on intensive care unit (ICU)-bed occupancy. While lockdown is effective in containing the viral spread, once lifted, regardless of duration, it would be unlikely to prevent a rebound. Both physical distancing and mask-wearing, although effective in slowing the epidemic and in reducing mortality, would also be ineffective in ultimately preventing ICUs from becoming overwhelmed and a subsequent second lockdown. However, these measures coupled with the shielding of vulnerable people would be associated with better outcomes, including lower mortality and maintaining an adequate ICU capacity to prevent a second lockdown. Benefits would nonetheless be markedly reduced if most people do not adhere to these measures, or if they are not maintained for a sufficiently long period.