Influenza epidemics each year cause hundreds of thousands of deaths worldwide and put high loads on health care systems, in France and elsewhere. A main concern for resource planning in public health is the risk of an extreme and dangerous epidemic. Sizes of epidemics are measured by the number of visits to doctors caused by Influenza Like Illness (ILI), and health care planning relies on prediction of ILI rates. We use recent results on the multivariate Generalized Pareto (GP) distributions in Extreme Value Statistics to develop methods for real-time prediction of risks of exceeding very high levels and for detection of unusual and potentially very dangerous epidemics. Based on the observation of the two first weeks of the epidemic, the GP method for real-time prediction is employed to predict ILI rates of the third week and the total size of the epidemic for extreme influenza epidemics in France. We then apply a general anomaly detection framework to the ILI rates during the three first weeks of the epidemic for early detection of unusual extreme epidemics. As an additional input to resource planning we use standard methods from extreme value statistics to estimate risk of exceedance of high ILI levels in future years. The new methods are expected to be broadly applicable in health care planning and in many other areas of science and technology.