Climate change, technological innovation, as well as electrification of energy services to meet carbon targets, have a significant impact on electricity demand magnitude and patterns. Increasing generation from renewable energy sources is already changing supply variability at the hourly and seasonal timescales. Our aim is to conduct a rigorous study of European historical demand, to understand its relationship with social and weather drivers and, therefore, to gain insights into appropriate storage needs. Daily activity profiles exhibit notable differences across European countries, with some of them reporting a consistent demand reduction, up to 25%, during school closures and Christmas festivities. In addition, temperature sensitivity differentiates demand by countries' latitude (north vs. south), and by technologies (electric heating vs. other fuel based heating). Assuming a 100% renewables scenario, European countries would display quite distinct periodicities and amplitudes of their residual electricity demands. Annual load curves and temperature sensitivities of nations with high electric heating or cooling demand can assist in the prediction of future electricity and other fuel consumption under increased electrification and climate change scenarios. Fourier periodicity and residual demand analysis suggest that, in addition to grid storage, European countries with mutual energy needs in terms of seasonal demand and generation surplus might benefit from international trade to balance unmet demand. Our study of consumption variability in response to social and weather drivers constitutes a valuable resource to formulate country-specific demand scenarios, as well as to improve the design of energy system models.