UAV vision-language navigation (VLN) requires an agent to navigate complex 3D environments from an egocentric perspective while following ambiguous multi-step instructions over long horizons. Existing zero-shot methods remain limited, as they often rely on large base models, generic prompts, and loosely coordinated modules. In this work, we propose FineCog-Nav, a top-down framework inspired by human cognition that organizes navigation into fine-grained modules for language processing, perception, attention, memory, imagination, reasoning, and decision-making. Each module is driven by a moderate-sized foundation model with role-specific prompts and structured input-output protocols, enabling effective collaboration and improved interpretability. To support fine-grained evaluation, we construct AerialVLN-Fine, a curated benchmark of 300 trajectories derived from AerialVLN, with sentence-level instruction-trajectory alignment and refined instructions containing explicit visual endpoints and landmark references. Experiments show that FineCog-Nav consistently outperforms zero-shot baselines in instruction adherence, long-horizon planning, and generalization to unseen environments. These results suggest the effectiveness of fine-grained cognitive modularization for zero-shot aerial navigation. Project page: https://smartdianlab.github.io/projects-FineCogNav.