Removing fence occlusions from single images is a challenging task that degrades visual quality and limits downstream computer vision applications. Existing methods often fail on static scenes or require motion cues from multiple frames. To overcome these limitations, we introduce the first framework to leverage dual-pixel (DP) sensors for this problem. We propose Freq-DP Net, a novel dual-branch network that fuses two complementary priors: a geometric prior from defocus disparity, modeled using an explicit cost volume, and a structural prior of the fence's global pattern, learned via Fast Fourier Convolution (FFC). An attention mechanism intelligently merges these cues for highly accurate fence segmentation. To validate our approach, we build and release a diverse benchmark with different fence varieties. Experiments demonstrate that our method significantly outperforms strong general-purpose baselines, establishing a new state-of-the-art for single-image, DP-based fence removal.