The integration of fully homomorphic encryption (FHE) in federated learning (FL) has led to significant advances in data privacy. However, during the aggregation phase, it often results in performance degradation of the aggregated model, hindering the development of robust representational generalization. In this work, we propose a novel multimodal quantum federated learning framework that utilizes quantum computing to counteract the performance drop resulting from FHE. For the first time in FL, our framework combines a multimodal quantum mixture of experts (MQMoE) model with FHE, incorporating multimodal datasets for enriched representation and task-specific learning. Our MQMoE framework enhances performance on multimodal datasets and combined genomics and brain MRI scans, especially for underrepresented categories. Our results also demonstrate that the quantum-enhanced approach mitigates the performance degradation associated with FHE and improves classification accuracy across diverse datasets, validating the potential of quantum interventions in enhancing privacy in FL.