Influence Maximization (IM), aiming to identify a small set of highly influential nodes in social networks, is a critical problem in graph analysis. Recently, Graph Neural Networks (GNNs) have demonstrated superior effectiveness in addressing IM. However, a trained GNN still raises significant privacy concerns, as it may expose sensitive node features and structural information. While Differential Privacy (DP) techniques have been widely applied to GNNs for node-level tasks, they cannot be directly extended to 1M problems. This is because IM requires more complex structural information for training, resulting in an extremely larger DP noise scale than node-level tasks. To tackle these issues, we propose PrivIM, a novel differentially private subgraph-based GNNs framework for IM tasks, which ensures node-level DP guarantees. Within PrivIM, we design a unique dual-stage adaptive frequency sampling scheme to optimize the model utility. First, it reduces the correlation between nodes by dynamically adjusting each node's sampling probability. Then additional subgraphs are incorporated to supplement boundary structural information, enhancing utility without increasing privacy budget. Extensive experiments on six real-world datasets demonstrate that PrivIM maintains high utility in IM compared to baseline methods.