Graph Neural Networks (GNNs) have demonstrated exceptional efficacy in relational learning tasks, including node classification and link prediction. However, their application raises significant fairness concerns, as GNNs can perpetuate and even amplify societal biases against protected groups defined by sensitive attributes such as race or gender. These biases are often inherent in the node features, structural topology, and message-passing mechanisms of the graph itself. A critical limitation of existing fairness-aware GNN methods is their reliance on the strong assumption that sensitive attributes are fully available for all nodes during training--a condition that poses a practical impediment due to privacy concerns and data collection constraints. To address this gap, we propose a novel, model-agnostic fairness regularization framework designed for the realistic scenario where sensitive attributes are only partially available. Our approach formalizes a fairness-aware objective function that integrates both equal opportunity and statistical parity as differentiable regularization terms. Through a comprehensive empirical evaluation across five real-world benchmark datasets, we demonstrate that the proposed method significantly mitigates bias across key fairness metrics while maintaining competitive node classification performance. Results show that our framework consistently outperforms baseline models in achieving a favorable fairness-accuracy trade-off, with minimal degradation in predictive accuracy. The datasets and source code will be publicly released at https://github.com/mtavassoli/GNN-FC.