Text simplification supports second language (L2) learning by providing comprehensible input, consistent with the Input Hypothesis. However, constructing personalized parallel corpora is costly, while existing large language model (LLM)-based readability control methods rely on pre-labeled sentence corpora and primarily target English. We propose Re-RIGHT, a unified reinforcement learning framework for adaptive multilingual text simplification without parallel corpus supervision. We first show that prompting-based lexical simplification at target proficiency levels (CEFR, JLPT, TOPIK, and HSK) performs poorly at easier levels and for non-English languages, even with state-of-the-art LLMs such as GPT-5.2 and Gemini 2.5. To address this, we collect 43K vocabulary-level data across four languages (English, Japanese, Korean, and Chinese) and train a compact 4B policy model using Re-RIGHT, which integrates three reward modules: vocabulary coverage, semantic preservation, and coherence. Compared to the stronger LLM baselines, Re-RIGHT achieves higher lexical coverage at target proficiency levels while maintaining original meaning and fluency.