Malicious attacks on vehicular networks pose a serious threat to road safety as well as communication reliability. A major source of these threats stems from misbehaving vehicles within the network. To address this challenge, we propose a Large Language Model (LLM)-empowered Misbehavior Detection System (MDS) within an edge-cloud detection framework. Specifically, we fine-tune Mistral-7B, a compact and high-performing LLM, to detect misbehavior based on Basic Safety Messages (BSM) sequences as the edge component for real-time detection, while a larger LLM deployed in the cloud validates and reinforces the edge model's detection through a more comprehensive analysis. By updating only 0.012% of the model parameters, our model, which we named MistralBSM, achieves 98% accuracy in binary classification and 96% in multiclass classification on a selected set of attacks from VeReMi dataset, outperforming LLAMA2-7B and RoBERTa. Our results validate the potential of LLMs in MDS, showing a significant promise in strengthening vehicular network security to better ensure the safety of road users.