The share of renewable energy sources (RES) in the global energy system is systematically increasing, making them the most important element of the energy transformation. Their use enables rational management of limited resources, reduction of environmental pollution, and has a significant inhibitory effect on energy poverty by improving energy efficiency. The aim of this article is to assess the impact of the use of renewable energy on the level of energy poverty in the European Union countries in 2010, 2015, and 2022. A taxonomic measure of development based on the Weber median was used to examine the relationship between the results achieved by individual EU member states in terms of the impact of the use of renewable energy on the level of energy poverty. The research results clearly indicate the existence of disproportions between the countries of the “old” EU and the countries that joined it in 2004 and later. These disproportions concern both the use of energy obtained from renewable sources and energy poverty. In the countries of the “old” Union, a positive moderate relationship was identified between the use of renewable energy and energy poverty, which means that a higher share of the use of energy from renewable sources in these countries reduces energy poverty. In the countries of the “new” Union, however, this relationship was very weak (2010) or non-existent. Since the renewable energy sector is subject to government policy and regulations, the results presented in this paper should be of interest to decision-makers. A stable, long-term policy should provide an appropriate investment climate that provides support for renewable energy projects and reduces the level of energy poverty.