While COVID-19 was already responsible for more than 500,000 deaths worldwide as of July 3, 2020, very little is known on the socio-economic heterogeneity of its impact on mortality. In this paper, we combine several administrative data sources to estimate the relationship between mortality due to COVID-19 and poverty at a very local level (i.e. the municipality level) in France, one of the most severely hit country in the world. We nd strong evidence of an income gradient in the impact of the pandemic on mortality: it is twice as large in the poorest municipalities compared to other municipalities. We then show that both poor housing conditions and higher occupational exposure are likely mechanisms. Overall, these mechanisms accounts for up to 60% of the difference observed between rich and poor municipalities.