Cross-Domain Few-Shot Learning (CDFSL) adapts models trained with large-scale general data (source domain) to downstream target domains with only scarce training data, where the research on vision-language models (e.g., CLIP) is still in the early stages. Typical downstream domains, such as medical diagnosis, require fine-grained visual cues for interpretable recognition, but we find that current fine-tuned CLIP models can hardly focus on these cues, albeit they can roughly focus on important regions in source domains. Although current works have demonstrated CLIP's shortcomings in capturing local subtle patterns, in this paper, we find that the domain gap and scarce training data further exacerbate such shortcomings, much more than that of holistic patterns, which we call the local misalignment problem in CLIP-based CDFSL. To address this problem, due to the lack of supervision in aligning local visual features and text semantics, we turn to self-supervision information. Inspired by the translation task, we propose the CC-CDFSL method with cycle consistency, which translates local visual features into text features and then translates them back into visual features (and vice versa), and constrains the original features close to the translated back features. To reduce the noise imported by richer information in the visual modality, we further propose a Semantic Anchor mechanism, which first augments visual features to provide a larger corpus for the text-to-image mapping, and then shrinks the image features to filter out irrelevant image-to-text mapping. Extensive experiments on various benchmarks, backbones, and fine-tuning methods show we can (1) effectively improve the local vision-language alignment, (2) enhance the interpretability of learned patterns and model decisions by visualizing patches, and (3) achieve state-of-the-art performance.