Open-vocabulary semantic segmentation requires assigning pixel-level semantic labels while supporting an open and unrestricted set of categories. Training-free CLIP-based approaches preserve strong zero-shot generalization but typically rely on a single inference mechanism, limiting their ability to jointly address unreliable local tokens and insufficient spatial coherence. We propose DouC, a training-free dual-branch CLIP framework that decomposes dense prediction into two complementary components. OG-CLIP improves patch-level reliability via lightweight, inference-time token gating, while FADE-CLIP injects external structural priors through proxy attention guided by frozen vision foundation models. The two branches are fused at the logit level, enabling local token reliability and structure-aware patch interactions to jointly influence final predictions, with optional instance-aware correction applied as post-processing. DouC introduces no additional learnable parameters, requires no retraining, and preserves CLIP's zero-shot generalization. Extensive experiments across eight benchmarks and multiple CLIP backbones demonstrate that DouC consistently outperforms prior training-free methods and scales favorably with model capacity.