The optimization of urban traffic is threatened by the complexity of achieving a balance between transport efficiency and the maintenance of privacy, as well as the equitable distribution of traffic based on socioeconomically diverse neighborhoods. Current centralized traffic management schemes invade user location privacy and further entrench traffic disparity by offering disadvantaged route suggestions, whereas current federated learning frameworks do not consider fairness constraints in multi-objective traffic settings. This study presents a privacy-preserving federated learning framework, termed FedFair-Traffic, that jointly and simultaneously optimizes travel efficiency, traffic fairness, and differential privacy protection. This is the first attempt to integrate three conflicting objectives to improve urban transportation systems. The proposed methodology enables collaborative learning between related vehicles with data locality by integrating Graph Neural Networks with differential privacy mechanisms ($ε$-privacy guarantees) and Gini coefficient-based fair constraints using multi-objective optimization. The framework uses federated aggregation methods of gradient clipping and noise injection to provide differential privacy and optimize Pareto-efficient solutions for the efficiency-fairness tradeoff. Real-world comprehensive experiments on the METR-LA traffic dataset showed that FedFair-Traffic can reduce the average travel time by 7\% (14.2 minutes) compared with their centralized baselines, promote traffic fairness by 73\% (Gini coefficient, 0.78), and offer high privacy protection (privacy score, 0.8) with an 89\% reduction in communication overhead. These outcomes demonstrate that FedFair-Traffic is a scalable privacy-aware smart city infrastructure with possible use-cases in metropolitan traffic flow control and federated transportation networks.