Purpose: The treatment of cardiovascular diseases requires complex and challenging navigation of a guidewire and catheter. This often leads to lengthy interventions during which the patient and clinician are exposed to X-ray radiation. Deep Reinforcement Learning approaches have shown promise in learning this task and may be the key to automating catheter navigation during robotized interventions. Yet, existing training methods show limited capabilities at generalizing to unseen vascular anatomies, requiring to be retrained each time the geometry changes. Methods: In this paper, we propose a zero-shot learning strategy for three-dimensional autonomous endovascular navigation. Using a very small training set of branching patterns, our reinforcement learning algorithm is able to learn a control that can then be applied to unseen vascular anatomies without retraining. Results: We demonstrate our method on 4 different vascular systems, with an average success rate of 95% at reaching random targets on these anatomies. Our strategy is also computationally efficient, allowing the training of our controller to be performed in only 2 hours. Conclusion: Our training method proved its ability to navigate unseen geometries with different characteristics, thanks to a nearly shape-invariant observation space.