View-Guided Point Cloud Completion (VG-PCC) aims to reconstruct complete point clouds from partial inputs by referencing single-view images. While existing VG-PCC models perform well on in-class predictions, they exhibit significant performance drops when generalizing to unseen categories. We identify two key limitations underlying this challenge: (1) Current encoders struggle to bridge the substantial modality gap between images and point clouds. Consequently, their learned representations often lack robust cross-modal alignment and over-rely on superficial class-specific patterns. (2) Current decoders refine global structures holistically, overlooking local geometric patterns that are class-agnostic and transferable across categories. To address these issues, we present a novel generalizable VG-PCC framework for unseen categories based on Geometric Alignment and Prior Modulation (GAPM). First, we introduce a Geometry Aligned Encoder that lifts reference images into 3D space via depth maps for natural alignment with the partial point clouds. This reduces dependency on class-specific RGB patterns that hinder generalization to unseen classes. Second, we propose a Prior Modulated Decoder that incorporates class-agnostic local priors to reconstruct shapes on a regional basis. This allows the adaptive reuse of learned geometric patterns that promote generalization to unseen classes. Extensive experiments validate that GAPM consistently outperforms existing models on both seen and, notably, unseen categories, establishing a new benchmark for unseen-category generalization in VG-PCC. Our code can be found in the supplementary material.