Ensuring the authenticity of video content remains challenging as DeepFake generation becomes increasingly realistic and robust against detection. Most existing detectors implicitly assume temporally consistent and clean facial sequences, an assumption that rarely holds in real-world scenarios where compression artifacts, occlusions, and adversarial attacks destabilize face detection and often lead to invalid or misdetected faces. To address these challenges, we propose a Laplacian-Regularized Graph Convolutional Network (LR-GCN) that robustly detects DeepFakes from noisy or unordered face sequences, while being trained only on clean facial data. Our method constructs an Order-Free Temporal Graph Embedding (OF-TGE) that organizes frame-wise CNN features into an adaptive sparse graph based on semantic affinities. Unlike traditional methods constrained by strict temporal continuity, OF-TGE captures intrinsic feature consistency across frames, making it resilient to shuffled, missing, or heavily corrupted inputs. We further impose a dual-level sparsity mechanism on both graph structure and node features to suppress the influence of invalid faces. Crucially, we introduce an explicit Graph Laplacian Spectral Prior that acts as a high-pass operator in the graph spectral domain, highlighting structural anomalies and forgery artifacts, which are then consolidated by a low-pass GCN aggregation. This sequential design effectively realizes a task-driven spectral band-pass mechanism that suppresses background information and random noise while preserving manipulation cues. Extensive experiments on FF++, Celeb-DFv2, and DFDC demonstrate that LR-GCN achieves state-of-the-art performance and significantly improved robustness under severe global and local disruptions, including missing faces, occlusions, and adversarially perturbed face detections.