Generative adversarial networks (GANs) are increasingly used for synthetic data generation in privacy-sensitive domains, yet their fairness implications under formal privacy guarantees remain underexplored. This paper presents a systematic study of how differential privacy (DP) in private GANs influences fairness across multiple datasets and sensitive attributes. We evaluate differentially private GANs against group and individual fairness metrics, along with privacy and utility benchmarks. Our results show that while stricter DP guarantees often reduce data utility, their effects on fairness are inconsistent, sometimes amplifying disparities rather than mitigating them. We further demonstrate that balancing sensitive attributes can improve group fairness but may worsen individual fairness, highlighting a trade-off shaped by dataset structure.