This work introduces SAM-LLM, a novel hybrid architecture that bridges the gap between the contextual reasoning of Large Language Models (LLMs) and the physical precision of kinematic lane change models for autonomous driving. The system is designed for interpretable lane change trajectory prediction by finetuning an LLM to output the core physical parameters of a trajectory model instead of raw coordinates. For lane-keeping scenarios, the model predicts discrete coordinates, but for lane change maneuvers, it generates the parameters for an enhanced Sinusoidal Acceleration Model (SAM), including lateral displacement, maneuver duration, initial lateral velocity, and longitudinal velocity change. This parametric approach yields a complete, continuous, and physically plausible trajectory model that is inherently interpretable and computationally efficient, achieving an 80% reduction in output size compared to coordinate-based methods. The SAM-LLM achieves a state-of-the-art overall intention prediction accuracy of 98.73%, demonstrating performance equivalent to traditional LLM predictors while offering significant advantages in explainability and resource efficiency.