Traditional topic models often struggle with contextual nuances and fail to adequately handle polysemy and rare words. This limitation typically results in topics that lack coherence and quality. Large Language Models (LLMs) can mitigate this issue by generating an initial set of topics. However, these raw topics frequently lack refinement and representativeness, which leads to redundancy without lexical similarity and reduced interpretability. This paper introduces HAMLET, a graph-driven architecture for cross-lingual healthcare topic modeling that uses LLMs. The proposed approach leverages neural-enhanced semantic fusion to refine the embeddings of topics generated by the LLM. Instead of relying solely on statistical co-occurrence or human interpretation to extract topics from a document corpus, this method introduces a topic embedding refinement that uses Bidirectional Encoder Representations from Transformers (BERT) and Graph Neural Networks (GNN). After topic generation, a hybrid technique that involves BERT and Sentence-BERT (SBERT) is employed for embedding. The topic representations are further refined using a GNN, which establishes connections between documents, topics, words, similar topics, and similar words. A novel method is introduced to compute similarities. Consequently, the topic embeddings are refined, and the top k topics are extracted. Experiments were conducted using two healthcare datasets, one in English and one in French, from which six sets were derived. The results demonstrate the effectiveness of HAMLET.