Large Language Models have achieved remarkable success in language understanding and reasoning, and their multimodal extensions enable comprehension of images, video, and audio. Inspired by this, foundation models for brain functional connectivity networks derived from resting-state fMRI have shown promise in clinical tasks. However, existing methods do not align FCNs with the text modality, limiting the ability of LLMs to directly understand FCNs. To address this, we propose FCN-LLM, a framework that enables LLMs to understand FCNs through graph-level, multi-task instruction tuning. Our approach employs a multi-scale FCN encoder capturing brain-region, functional subnetwork, and whole-brain features, projecting them into the semantic space of LLM. We design multi-paradigm instruction tasks covering 19 subject-specific attributes across demographics, phenotypes, and psychiatric conditions. A multi-stage learning strategy first aligns FCN embeddings with the LLM and then jointly fine-tunes the entire model to capture high-level semantic information. Experiments on a large-scale, multi-site FCN database show that FCN-LLM achieves strong zero-shot generalization on unseen datasets, outperforming conventional supervised and foundation models. This work introduces a new paradigm for integrating brain functional networks with LLMs, offering a flexible and interpretable framework for neuroscience.