Effective and timely disease surveillance systems have the potential to help public health officials design interventions to mitigate the effects of disease outbreaks. Currently, healthcare-based disease monitoring systems in France offer influenza activity information that lags real-time by one to three weeks. This temporal data gap introduces uncertainty that prevents public health officials from having a timely perspective on the population-level disease activity. Here, we present a machine-learning modeling approach that produces real-time estimates and short-term forecasts of influenza activity for the twelve continental regions of France by leveraging multiple disparate data sources that include, Google search activity, real-time and local weather information, flu-related Twitter micro-blogs, electronic health records data, and historical disease activity synchronicities across regions. Our results show that all data sources contribute to improving influenza surveillance and that machine-learning ensembles that combine all data sources lead to accurate and timely predictions.