To address the scale mismatch caused by large altitude variations in UAV visual place recognition, we propose a monocular vision-only altitude-adaptive geo-localization framework. The method first estimates relative altitude from a single downward-looking image by transforming the input into the frequency domain and formulating altitude estimation as a regression-as-classification (RAC) problem. The estimated altitude is then used to crop the query image to a canonical scale, after which a classification-then-retrieval visual place recognition module performs coarse localization. To improve retrieval robustness under varying image quality, we further introduce a quality-adaptive margin classifier (QAMC) and refine the final location by weighted coordinate estimation over the top retrieved candidates. Experiments on two synthetic datasets and two real-flight datasets show that the relative altitude estimation (RAE) module yields clear overall improvements in downstream retrieval performance under significant altitude changes. With our visual place recognition module, altitude adaptation improves average R@1 and R@5 by 41.50 and 56.83 percentage points, respectively, compared with using the same retrieval pipeline without altitude normalization, and the full system runs at 13.3 frames/s on the reported workstation hardware. These results indicate that relative altitude estimation provides an effective scale prior for cross-altitude UAV geo-localization and supports GPS-denied coarse initialization without auxiliary range sensors or temporal inputs.