Generating realistic and diverse trajectories is a critical challenge in autonomous driving simulation. While Large Language Models (LLMs) show promise, existing methods often rely on structured data like vectorized maps, which fail to capture the rich, unstructured visual context of a scene. To address this, we propose K-Gen, an interpretable keypoint-guided multimodal framework that leverages Multimodal Large Language Models (MLLMs) to unify rasterized BEV map inputs with textual scene descriptions. Instead of directly predicting full trajectories, K-Gen generates interpretable keypoints along with reasoning that reflects agent intentions, which are subsequently refined into accurate trajectories by a refinement module. To further enhance keypoint generation, we apply T-DAPO, a trajectory-aware reinforcement fine-tuning algorithm. Experiments on WOMD and nuPlan demonstrate that K-Gen outperforms existing baselines, highlighting the effectiveness of combining multimodal reasoning with keypoint-guided trajectory generation.