Function calling empowers large language models (LLMs) to interface with external tools, yet existing RL-based approaches suffer from misalignment between reasoning processes and tool-call decisions.We propose R2IF, a reasoning-aware RL framework for interpretable function calling, adopting a composite reward integrating format/correctness constraints, Chain-of-Thought Effectiveness Reward (CER), and Specification-Modification-Value (SMV) reward, optimized via GRPO.Experiments on BFCL/ACEBench show R2IF outperforms baselines by up to 34.62% (Llama3.2-3B on BFCL) with positive Average CoT Effectiveness (0.05 for Llama3.2-3B),enhancing both function-calling accuracy and interpretability for reliable tool-augmented LLM deployment.