The European Green Deal considers the increase in the share of renewable energy in final energy consumption (REFEC) among the main targets for achieving sustainable EU economies. In this context, the main aim of this paper is to provide an empirical evaluation of the relationship between GDP, global competitiveness index (GCI) and renewable energy consumption. According to panel data models based on the fully modified ordinary least squares method (FMOLS), there is a positive effect of renewable energy consumption progress on GDP and GCI growth, and also a positive influence of economic growth on renewable energy consumption in the period 2007–2019 in the EU countries. The energy consumption is more influenced by economic growth rather than economic competitiveness. Few scenarios were proposed for economic growth and share of renewable sources (RESs) in the final consumption using as forecasting method the proposed panel data models. The cluster analysis suggested two groups of countries according to RES share in gross final energy consumption (GFEC). The first group includes six countries (Sweden, Denmark, Finland, Latvia, Portugal and Austria) that fixed a target of 30% or more, while the second one refers to countries with lower targets. Some policy recommendations are provided for the EU countries to enhance the utilization of renewable energy.