Neuromorphic (brain-inspired) photonics accelerates AI1 with high-speed, energy-efficient solutions for RF communication2, image processing3,4, and fast matrix multiplication5,6. However, integrated neuromorphic photonic hardware faces size constraints that limit network complexity. Recent advances in photonic quantum hardware7 and performant trainable quantum circuits8 offer a path to more scalable photonic neural networks. Here, we show that a combination of classical network layers with trainable continuous variable quantum circuits yields hybrid networks with improved trainability and accuracy. On a classification task, these hybrid networks match the performance of classical networks nearly twice their size. These performance benefits remain even when evaluated at state-of-the-art bit precisions for classical and quantum hardware. Finally, we outline available hardware and a roadmap to hybrid architectures. These hybrid quantum-classical networks demonstrate a unique route to enhance the computational capacity of integrated photonic neural networks without increasing the network size.