Federated learning (FL) has enabled training of multilingual large language models (LLMs) on diverse and decentralized multilingual data, especially on low-resource languages. To improve client-specific performance, personalization via the use of parameter-efficient fine-tuning (PEFT) modules such as LoRA is common. This involves a personalization strategy (PS), such as the design of the PEFT adapter structures (e.g., in which layers to add LoRAs and what ranks) and choice of hyperparameters (e.g., learning rates) for fine-tuning. Instead of manual PS configuration, we propose FedP²EFT, a federated learning-to-personalize method for multilingual LLMs in cross-device FL settings. Unlike most existing PEFT structure selection methods, which are prone to overfitting low-data regimes, FedP²EFT collaboratively learns the optimal personalized PEFT structure for each client via Bayesian sparse rank selection. Evaluations on both simulated and real-world multilingual FL benchmarks demonstrate that FedP²EFT largely outperforms existing personalized fine-tuning methods, while complementing other existing FL methods.