This paper investigates the challenges of developing large language models (LLMs) proficient in both multilingual understanding and medical knowledge. We demonstrate that simply translating medical data does not guarantee strong performance on clinical tasks in the target language. Our experiments reveal that the optimal language mix in training data varies significantly across different medical tasks. We find that larger models with carefully calibrated language ratios achieve superior performance on native-language clinical tasks. Furthermore, our results suggest that relying solely on fine-tuning may not be the most effective approach for incorporating new language knowledge into LLMs. Instead, data and computationally intensive pretraining methods may still be necessary to achieve optimal performance in multilingual medical settings. These findings provide valuable guidance for building effective and inclusive medical AI systems for diverse linguistic communities.