Federated learning (FL) addresses privacy concerns in training language models by enabling multiple clients to contribute to the training, without sending their data to others. However, non-IID (identically and independently distributed) data across clients often limits FL's performance. This issue is especially challenging during model fine-tuning, as noise due to variations in clients' data distributions can harm model convergence near stationary points. This paper proposes a targeted layer update strategy for fine-tuning in FL. Instead of randomly updating layers of the language model, as often done in practice, we use a scoring mechanism to identify and update the most critical layers, avoiding excessively noisy or even poisoned updates by freezing the parameters in other layers. We show in extensive experiments that our method improves convergence and performance in non-IID settings, offering a more efficient approach to fine-tuning federated language models.