Geometric correction of satellite images is an essential pre-processing step for accurate geospatial analysis, but non-experts often face practical limitations because detailed sensor models and Ground Control Point data are not readily accessible. Traditional methods rely on physical sensor models or the Rational Function Model (RFM) using vendor-provided Rational Polynomial Coefficients (RPC). However, this information is often unavailable or lacks sufficient accuracy. This paper proposes a two-stage framework that utilizes AI matching technologies and open access data to automatically correct satellite images lacking georeferencing information. In Stage 1, a coarse Affine correction is executed using SuperPoint and LightGlue with an open basemap (Sentinel-2). In Stage 2, precise corresponding points are extracted through patch-based hierarchical LoFTR matching, and 3D GCPs are generated utilizing the SRTM. Subsequently, sensor-independent RPC are robustly estimated through the rpcfit library, and the final geometrically corrected image is generated through resampling. This framework was verified by applying it to 4.8m resolution BlueBON satellite images that lack georeferencing information. In seven experimental regions with diverse geographical characteristics, an average Root Mean Square Error (RMSE) of 8.050m (1.68 pixels based on BlueBON resolution) referenced to the Sentinel-2 basemap, and an average of 9.02m (1.88 pixels) referenced to Google Maps, was achieved. This result demonstrates that it is possible to precisely correct 4.8m medium-resolution images using a 10m open basemap, providing a practical, accessible, and automated geometric correction solution for general users.