Future autonomous vehicles (AVs) will use a variety of sensors that generate a vast amount of data. Naturally, this data not only serves self-driving algorithms; but can also assist other vehicles or the infrastructure in real-time decision-making. Consequently, vehicles shall exchange their measurement data over Vehicle-to-Everything (V2X) technologies. Moreover, predicting the state of the road network might be beneficial too. With such a prediction, we might mitigate road congestion, balance parking lot usage, or optimize the traffic flow. That would decrease transportation costs as well as reduce its environmental impact. In this paper, we propose a federated measurement and learning system that provides real-time data to fellow vehicles over Vehicle-to-Vehicle (V2V) communication while also operating a federated learning (FL) scheme over the Vehicle-to-Network (V2N) link to create a predictive model of the transportation network. As we are yet to have real-world AV data, we model it with a non-IID (independent and identically distributed) dataset to evaluate the capabilities of the proposed system in terms of performance and privacy. Results indicate that the proposed FL scheme improves learning performance and prevents eavesdropping at the aggregator server side.