The current energy crisis has shown all states that energy from renewable sources can be a determining factor in the states’ sustainable development. Several papers have studied the relationship between renewable energy consumption and economic development, finding various situations, but there is no consensus. Thus, this study aims to first investigate the causal relationship between economic growth and total and sectoral renewable energy consumption (European Union and each Member State, for 2004–2020) by testing various linear and non-linear regressions to choose the fit model. Second, the investigation extends to analysing the impact of renewable energy consumption by sector on economic development. A hybrid approach is used, namely structural equation modelling and artificial neural networks. The study findings indicate the effect and the meaning (directly or inversely) exerted by the three sectoral components on economic growth, with different intensities from one country to another. There is a significant influence on the consumption of renewable energy in the heating and cooling sectors and transport on gross domestic product at the European Union level and for most member states. Based on the obtained results, a series of theoretical, practical, and political implications are provided.