During the COVID-19 pandemic, confinement measures were adopted across the world to limit the spread of the virus. In France, these measures were applied between March 17 and May 10. Using high-quality population census data and focusing on co-residence structures on French territory, this article analyzes how co-residence patterns unevenly put different socio-demographic groups at risk of being infected and dying from COVID-19. The research ambition is to quantify the possible impact of co-residence structures heterogeneity on socio-economic inequalities in mortality stemming from within-household transmission of the virus. Using a simulation approach, the article highlights the existence of theoretical pronounced inequalities of vulnerability to COVID-19 related to cohabitation structures as well as a reversal of the social gradient of vulnerability when the age of the infected person increases. Among young age categories, infection is simulated to lead to more deaths in the less educated or foreign-born populations. Among the older ones, the inverse holds with infections having a greater potential to provoke deaths through the transmission of the virus within households headed by a highly educated or a native-born person. Demographic patterns such as the cohabitation of multiple generations and the survival of both partners of a couple help to explain these results. Even though inter-generational co-residence and large households are more common among the lower educated and foreign born in general, the higher educated are more likely to still live with their partner at higher ages.