Software-Defined Networking (SDN) provides flexible and programmable network management; however, its centralized control architecture remains highly vulnerable to Distributed Denial-of-Service (DDoS) attacks, particularly Carpet-Bombing DDoS attacks that distribute malicious traffic across multiple targets to evade conventional detection mechanisms. In this paper, a Retrieval-Augmented Generation (RAG)-based framework is proposed for real-time detection and mitigation of Carpet-Bombing DDoS attacks in SDN environments. The proposed framework combines interface-level traffic features representation, semantic embedding generation, FAISS-based similarity retrieval, and Large Language Model (LLM)-driven contextual inference to classify traffic behavior without requiring conventional supervised model training or retraining. To evaluate the effectiveness of the proposed framework, extensive experiments were conducted under multiple Carpet-Bombing DDoS attack scenarios with different attack intensities. In addition, two traffic representation strategies, namely structured JSON-based representation and natural language-based representation (NLR), were investigated using multiple state-of-the-art LLMs. The experimental results demonstrate that the proposed framework achieved highly accurate and stable attack detection performance, while the framework configuration utilizing the Gemma-4-31B-IT model achieved the strongest overall detection results. Furthermore, real-time experiments confirmed the capability of the proposed framework to rapidly detect and mitigate Carpet-Bombing DDoS attacks while maintaining stable SDN network operation. The obtained results highlight the effectiveness of integrating RAG mechanisms with LLM for intelligent and adaptive SDN security analysis.