Accurate 3D plant models are crucial for computational phenotyping and physics-based simulation; however, current approaches face significant limitations. Learning-based reconstruction methods require extensive species-specific training data and lack editability. Procedural modeling offers parametric control but demands specialized expertise in geometric modeling and an in-depth understanding of complex procedural rules, making it inaccessible to domain scientists. We present FloraForge, an LLM-assisted framework that enables domain experts to generate biologically accurate, fully parametric 3D plant models through iterative natural language Plant Refinements (PR), minimizing programming expertise. Our framework leverages LLM-enabled co-design to refine Python scripts that generate parameterized plant geometries as hierarchical B-spline surface representations with botanical constraints with explicit control points and parametric deformation functions. This representation can be easily tessellated into polygonal meshes with arbitrary precision, ensuring compatibility with functional structural plant analysis workflows such as light simulation, computational fluid dynamics, and finite element analysis. We demonstrate the framework on maize, soybean, and mung bean, fitting procedural models to empirical point cloud data through manual refinement of the Plant Descriptor (PD), human-readable files. The pipeline generates dual outputs: triangular meshes for visualization and triangular meshes with additional parametric metadata for quantitative analysis. This approach uniquely combines LLM-assisted template creation, mathematically continuous representations enabling both phenotyping and rendering, and direct parametric control through PD. The framework democratizes sophisticated geometric modeling for plant science while maintaining mathematical rigor.