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This paper describes the geography of multi-dimensional poverty across French communes in 2017. We build an extended data set documenting 7 key dimensions of well-being (income, unemployment, housing, education, civic engagement, life expectancy and air quality) in about 35,000 communes. Life expectancy at commune-level is obtained from an original small-area estimation method combining commune and department-level data. We derive an index of multi-dimensional poverty to provide an unprecedented degree of granularity in the description of spatial inequality and poverty in France. The results show that joint deprivation in at least 5 dimensions of well-being is starkly concentrated among 316 communes, representing as much as 5.2 million inhabitants (7.7% of the French population). About 70% of these people are also in extreme poverty, which suggests that the concepts of multi-dimensional poverty and extreme income poverty significantly overlap. [ABSTRACT FROM AUTHOR]