Unmanned aerial vehicles (UAVs) in flying ad-hoc networks (FANETs) face security challenges due to the dynamic and distributed nature of these networks. This paper presents the Federated Learning-based Intrusion Detection System (FL-IDS), an innovative approach designed to improve FANET security. FL-IDS leverages federated learning to address privacy concerns of centralized intrusion detection systems. FL-IDS operates in a decentralized manner, enabling UAVs to collaboratively train a global intrusion detection model without sharing raw data. Local models are assigned to each UAV, using client-specific data, and only updated model weights are shared with a central server. This preserves privacy while utilizing collective intelligence for effective intrusion detection. Experimental results show FL-IDS's competitive performance with Central IDS (C-IDS) while mitigating privacy concerns. The Bias Towards Specific Clients (BTSC) method further enhances FL-IDS performance, surpassing C-IDS even at lower attacker ratios. A comparative analysis with traditional intrusion detection methods, including Local IDS (L-IDS), provides insights into FL-IDS's strengths. This study significantly contributes to FANET security by introducing a privacy-aware, decentralized intrusion detection approach tailored to the unique challenges of UAV networks.