Large Language Models (LLMs) are increasingly leveraged for translation tasks but often fall short when translating inclusive language -- such as texts containing the singular 'they' pronoun or otherwise reflecting fair linguistic protocols. Because these challenges span both computational and societal domains, it is imperative to critically evaluate how well LLMs handle inclusive translation with a well-founded framework. This paper presents FairTranslate, a novel, fully human-annotated dataset designed to evaluate non-binary gender biases in machine translation systems from English to French. FairTranslate includes 2418 English-French sentence pairs related to occupations, annotated with rich metadata such as the stereotypical alignment of the occupation, grammatical gender indicator ambiguity, and the ground-truth gender label (male, female, or inclusive). We evaluate four leading LLMs (Gemma2-2B, Mistral-7B, Llama3.1-8B, Llama3.3-70B) on this dataset under different prompting procedures. Our results reveal substantial biases in gender representation across LLMs, highlighting persistent challenges in achieving equitable outcomes in machine translation. These findings underscore the need for focused strategies and interventions aimed at ensuring fair and inclusive language usage in LLM-based translation systems. We make the FairTranslate dataset publicly available on Hugging Face, and disclose the code for all experiments on GitHub.