Unmanned Aerial Vehicle (UAV)-assisted networks are increasingly foreseen as a promising approach for emergency response, providing rapid, flexible, and resilient communications in environments where terrestrial infrastructure is degraded or unavailable. In such scenarios, voice radio communications remain essential for first responders due to their robustness; however, their unstructured nature prevents direct integration with automated UAV-assisted network management. This paper proposes SIREN, an AI-driven framework that enables voice-driven perception for UAV-assisted networks. By integrating Automatic Speech Recognition (ASR) with Large Language Model (LLM)-based semantic extraction and Natural Language Processing (NLP) validation, SIREN converts emergency voice traffic into structured, machine-readable information, including responding units, location references, emergency severity, and Quality-of-Service (QoS) requirements. SIREN is evaluated using synthetic emergency scenarios with controlled variations in language, speaker count, background noise, and message complexity. The results demonstrate robust transcription and reliable semantic extraction across diverse operating conditions, while highlighting speaker diarization and geographic ambiguity as the main limiting factors. These findings establish the feasibility of voice-driven situational awareness for UAV-assisted networks and show a practical foundation for human-in-the-loop decision support and adaptive network management in emergency response operations.