The North Atlantic eddy‐driven jet (EDJ) is the main driver of winter weather in Europe and has often been described by its latitude or strength. Here, we show that the influence of the EDJ on European winter temperature extremes can be better characterized by a multiparametric perspective that accounts for additional aspects of the EDJ structure (tilt, zonal elongation, etc.). We identify four regions where extreme temperatures are distinctly associated with the EDJ: Scandinavia, Central Europe, Eastern Europe, and Western Mediterranean (WMED). Overall, the anomalous horizontal advection induced by blockings during cold spells and enhanced westerlies during warm events is the main mechanism leading to extreme event occurrence. However, diabatic processes play an important role in WMED region. Both processes generate asymmetric effects in minimum and maximum temperatures contributing to higher intensities of cold than warm events. These extreme events are associated with different EDJ configurations, which typically involve perturbed EDJs during cold spells and strong tilted EDJs during warm events, but with important variations depending on the region. In almost every region, the combined effects of more than two EDJ parameters yield significant increases in the probability of cold and warm events, suggesting an oversimplification of traditional approaches based on a single EDJ parameter. We show, using logistic regression models, that, although important, latitude and intensity are often unable to discriminate unequivocally the region of extreme event occurrence, and in some regions, they do not drive the largest changes in the odds of extremes.