Zero-shot video moment retrieval (ZVMR) is the task of localizing a temporal moment within an untrimmed video using a natural language query without relying on task-specific training data. The primary challenge in this setting lies in the mismatch in semantic granularity between textual queries and visual content. Previous studies in ZVMR have attempted to achieve alignment by leveraging high-quality pre-trained knowledge that represents video and language in a joint space. However, these approaches failed to balance the semantic granularity between the pre-trained knowledge provided by each modality for a given scene. As a result, despite the high quality of each modality's representations, the mismatch in granularity led to inaccurate retrieval. In this paper, we propose a training-free framework, called Granularity-Aware Alignment (GranAlign), that bridges this gap between coarse and fine semantic representations. Our approach introduces two complementary techniques: granularity-based query rewriting to generate varied semantic granularities, and query-aware caption generation to embed query intent into video content. By pairing multi-level queries with both query-agnostic and query-aware captions, we effectively resolve semantic mismatches. As a result, our method sets a new state-of-the-art across all three major benchmarks (QVHighlights, Charades-STA, ActivityNet-Captions), with a notable 3.23% mAP@avg improvement on the challenging QVHighlights dataset.