Aerial-Ground person re-identification (AG-ReID) is an emerging yet challenging task that aims to match pedestrian images captured from drastically different viewpoints, typically from unmanned aerial vehicles (UAVs) and ground-based surveillance cameras. The task poses significant challenges due to extreme viewpoint discrepancies, occlusions, and domain gaps between aerial and ground imagery. While prior works have made progress by learning cross-view representations, they remain limited in handling severe pose variations and spatial misalignment. To address these issues, we propose a Geometric and Semantic Alignment Network (GSAlign) tailored for AG-ReID. GSAlign introduces two key components to jointly tackle geometric distortion and semantic misalignment in aerial-ground matching: a Learnable Thin Plate Spline (LTPS) Module and a Dynamic Alignment Module (DAM). The LTPS module adaptively warps pedestrian features based on a set of learned keypoints, effectively compensating for geometric variations caused by extreme viewpoint changes. In parallel, the DAM estimates visibility-aware representation masks that highlight visible body regions at the semantic level, thereby alleviating the negative impact of occlusions and partial observations in cross-view correspondence. A comprehensive evaluation on CARGO with four matching protocols demonstrates the effectiveness of GSAlign, achieving significant improvements of +18.8\% in mAP and +16.8\% in Rank-1 accuracy over previous state-of-the-art methods on the aerial-ground setting.