Bridging 2D and 3D sensor modalities is critical for robust perception in autonomous systems. However, image-to-point cloud (I2P) registration remains challenging due to the semantic-geometric gap between texture-rich but depth-ambiguous images and sparse yet metrically precise point clouds, as well as the tendency of existing methods to converge to local optima. To overcome these limitations, we introduce CrossI2P, a self-supervised framework that unifies cross-modal learning and two-stage registration in a single end-to-end pipeline. First, we learn a geometric-semantic fused embedding space via dual-path contrastive learning, enabling annotation-free, bidirectional alignment of 2D textures and 3D structures. Second, we adopt a coarse-to-fine registration paradigm: a global stage establishes superpoint-superpixel correspondences through joint intra-modal context and cross-modal interaction modeling, followed by a geometry-constrained point-level refinement for precise registration. Third, we employ a dynamic training mechanism with gradient normalization to balance losses for feature alignment, correspondence refinement, and pose estimation. Extensive experiments demonstrate that CrossI2P outperforms state-of-the-art methods by 23.7% on the KITTI Odometry benchmark and by 37.9% on nuScenes, significantly improving both accuracy and robustness.