Modern localization relies on satellite and terrestrial infrastructures (e.g., global navigation satellite system (GNSS) and crowd-sourced Wi-Fi), supporting critical applications ranging from autonomous navigation to life services. However, they are susceptible to multimodal location spoofing attacks, where various types of wireless signals are crafted in a coordinated manner to deceive the receiver position. Such attacks can cause severe disruptions, such as misguiding vehicles and enabling fraud. Although recent deep learning methods help detect GNSS spoofing and jamming, they require extensive labeled datasets, they are not designed for multimodal location spoofing, training is computationally intensive and centralized, thus raising privacy concerns due to the sensitive nature of location data. We propose FedRAIM, a novel federated learning framework designed for robust, efficient, and privacy-preserving multimodal location spoofing detection. The key FedRAIM elements are: training labels are autonomously generated through an extended receiver autonomous integrity monitoring (RAIM) algorithm, incorporating diverse opportunistic information, i.e., terrestrial infrastructure signals, onboard sensor data, and naturally GNSS signals. During federated training, local long short-term memory (LSTM) models are trained independently on client devices. Server then aggregates, using the FedAvg algorithm, these local model parameters, not data, into a global model, which is subsequently distributed back to the clients for iterative training. Experimental results on real-world multimodal spoofing datasets demonstrate that FedRAIM achieves an area under the curve (AUC) of up to 98.3%.