Few-shot graph learning remains a fundamental yet challenging problem, especially under heterophilic graph settings where connected nodes are likely to belong to different classes. In such scenarios, two key challenges arise: (1) unreliable or noisy graph structures that hinder effective message passing, and (2) semantic inconsistency: in heterophilic graphs, aggregating messages from neighbors of different classes entangles representations and introduces misleading semantics. These issues are further exacerbated by the limited labeled data inherent to few-shot learning, making it difficult to adaptively repair structure or disentangle semantics. To address these challenges, we propose DAPrompt, a Dual Alignment Prompt framework that jointly calibrates graph structure and semantic representations across the learning pipeline. In the pretraining stage, DAPrompt incorporates a graph structure learning module to denoise and repair the underlying topology, enhancing structural reliability. In the prompt tuning stage, we introduce two coordinated modules: a structure-aware prompt learner, which employs prompt tokens to repair unreliable graph structures and capture structure-level alignment, and a semantics-aligned prompt learner, which enhances the graph using target node semantics to mitigate representation noise caused by class-mismatched propagation. Extensive experiments on both node-level and graph-level few-shot benchmarks validate its effectiveness, achieving state-of-the-art performance and highlighting the value of structure-semantic dual alignment in heterophilic few-shot graph learning.