We present Points2Plans, a framework for composable planning with a relational dynamics model that enables robots to solve long-horizon manipulation tasks from partial-view point clouds. Given a language instruction and a point cloud of the scene, our framework initiates a hierarchical planning procedure, whereby a language model generates a high-level plan and a sampling-based planner produces constraint-satisfying continuous parameters for manipulation primitives sequenced according to the high-level plan. Key to our approach is the use of a relational dynamics model as a unifying interface between the continuous and symbolic representations of states and actions, thus facilitating language-driven planning from high-dimensional perceptual input such as point clouds. Whereas previous relational dynamics models require training on datasets of multi-step manipulation scenarios that align with the intended test scenarios, Points2Plans uses only single-step simulated training data while generalizing zero-shot to a variable number of steps during real-world evaluations. We evaluate our approach on tasks involving geometric reasoning, multi-object interactions, and occluded object reasoning in both simulated and real-world settings. Results demonstrate that Points2Plans offers strong generalization to unseen long-horizon tasks in the real world, where it solves over 85% of evaluated tasks while the next best baseline solves only 50%.