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Mixture-of-Experts (MoE) models have emerged as a dominant paradigm for efficient LLM scaling, yet adapting them to non-English downstream tasks remains challenging. Existing fine-tuning approaches treat MoE models as monolithic learners, ignoring the heterogeneous routing structure that develops during pretraining. We validate across multiple MoE models and downstream tasks that middle layers form a language-universal alignment zone where routing divergence strongly predicts per-language task performance gaps. Building on this observation, we propose RA-MoE (Routing-Aligned MoE Fine-Tuning), a three-stage framework that categorizes parallel task examples into a four-way taxonomy (cc/ci/ic/ii) based on correctness in English and the target language, identifies task-relevant experts in the middle layers, and augments standard SFT with a routing alignment loss that encourages target-language routing on ci-type examples to follow the English task-expert activation pattern. Experiments across three MoE models, three tasks, and six target languages demonstrate that RA-MoE consistently outperforms standard SFT and strong baselines including Routing Steering and RISE, with the ci proportion of a task-language pair serving as a reliable predictor of alignment benefit.