Differentially private federated learning (DP-FL) often suffers from slow convergence under tight privacy budgets because the noise required for privacy preservation degrades gradient quality. Although second-order optimization can accelerate training, existing approaches for DP-FL face significant scalability limitations: Newton-type methods require clients to compute Hessians, while feature covariance methods scale poorly with model dimension. We propose DP-FedSOFIM, a simple and scalable second-order optimization method for DP-FL. The method constructs an online regularized proxy for the Fisher information matrix at the server using only privatized aggregated gradients, capturing useful curvature information without requiring Hessian computations or feature covariance estimation. Efficient rank-one updates based on the Sherman-Morrison formula enable communication costs proportional to the model size and require only O(d) client-side memory. Because all curvature and preconditioning operations are performed at the server on already privatized gradients, DP-FedSOFIM introduces no additional privacy cost beyond the underlying privatized gradient release mechanism. Experiments on CIFAR-10 and PathMNIST show that DP-FedSOFIM converges faster and consistently achieves higher accuracy than DP-FedGD, DP-SCAFFOLD, and DP-FedFC across a range of privacy budgets, with particularly pronounced gains under stringent privacy constraints.