Real-world networks often benefit from capturing both local and global interactions. Inspired by multi-modal analysis in brain imaging, where structural and functional connectivity offer complementary views of network organization, we propose a graph neural network framework that generalizes this approach to other domains. Our method introduces a functional connectivity block based on persistent graph homology to capture global topological features. Combined with structural information, this forms a multi-modal architecture called Functional Connectivity Graph Neural Networks. Experiments show consistent performance gains over existing methods, demonstrating the value of brain-inspired representations for graph-level classification across diverse networks.