Is Paris a 15-minute city, where inhabitants can access essential amenities such as schools and shops with a 15-minute walk or bike ride? The concept of a 15-minute (more generally, X-minute) city was launched in the French capital and was part of the current mayor's plan in her latest reelection campaign. Yet, its fit with the existing urban structure had not been previously assessed. This article combines open map data from a large participatory project and geo-localized socioeconomic data from official statistics to fill this gap. We show that, while the city of Paris is rather homogeneous, it is nonetheless characterized by remarkable inequalities between a highly accessible city center (though with some internal differences in terms of types of amenities) and a less well-equipped periphery, where lower-income neighborhoods are more often found. The heterogeneity increases if we consider Paris together with its immediate surroundings, the "Petite Couronne", where large numbers of daily commuters and other users of city facilities live. We thus conclude that successful implementation of the X-minute-city concept requires addressing existing socioeconomic inequalities, and that especially in big cities, it should be extended beyond the narrow boundaries of the municipality itself to encompass the larger area around it.