The global crisis of language endangerment meets a technological turning point as Generative AI (GenAI) and Large Language Models (LLMs) unlock new frontiers in automating corpus creation, transcription, translation, and tutoring. However, this promise is imperiled by fragmented practices and the critical lack of a methodology to navigate the fraught balance between LLM capabilities and the profound risks of data scarcity, cultural misappropriation, and ethical missteps. This paper introduces a novel analytical framework that systematically evaluates GenAI applications against language-specific needs, embedding community governance and ethical safeguards as foundational pillars. We demonstrate its efficacy through the Te Reo Māori revitalization, where it illuminates successes, such as community-led Automatic Speech Recognition achieving 92% accuracy, while critically surfacing persistent challenges in data sovereignty and model bias for digital archives and educational tools. Our findings underscore that GenAI can indeed revolutionize language preservation, but only when interventions are rigorously anchored in community-centric data stewardship, continuous evaluation, and transparent risk management. Ultimately, this framework provides an indispensable toolkit for researchers, language communities, and policymakers, aiming to catalyze the ethical and high-impact deployment of LLMs to safeguard the world's linguistic heritage.