Coronary artery disease (CAD) remains one of the leading causes of death globally, highlighting the need for reliable predictive systems to support early diagnosis and risk assessment. While traditional machine learning models perform well on structured clinical data, large language models (LLMs) present new possibilities to interpret medical information expressed in natural language. In this work, we develop a hybrid framework that bridges structured clinical data and natural-language representations for CAD prediction. Using a publicly available dataset of 1,190 patient records with 11 clinical attributes, structured variables are converted into interpretable feature representations and synthetic clinical narratives using LLMs. A validation pipeline performs reverse extraction of clinical variables and computes a consistency score with the original records, achieving an average fidelity of 94.61%. We then evaluate four conventional machine learning models and compare their performance with LLM-based classification under zero-shot and few-shot prompting settings. We use two LLMs here, GPT and Gemini. Experimental results show that Random Forest achieves the highest accuracy. Despite this advantage, LLM-based classification remains beneficial in real-world clinical settings. This is because LLMs operate directly on natural language patient descriptions, meaning that sensitive numerical patient data such as exact lab values, blood pressure readings, and diagnostic codes are kept private. Findings suggest that combining structured clinical data with LLM-generated narratives can enable new directions for hybrid clinical prediction systems.