The growing sophistication of cyberattacks highlights the urgent need for robust and precise methods to detect malicious network traffic. Traditional approaches struggle with the complex patterns of modern threats and capturing nuanced inter-session relationships and coordinated behaviors. To address these challenges, we propose FlowGraphNet, a novel deep-learning framework for graph-based malicious traffic detection. FlowGraphNet segments network traffic into sessions, each transformed into a fixed-size grayscale image. A Convolutional Neural Network (CNN) then extracts detailed intra-session features. These high-level features construct a graph where sessions are nodes and edges capture learned feature similarities. A Graph Neural Network (GNN) then models inter-session relationships to detect collaborative or coordinated malicious behaviors. We evaluate FlowGraphNet on a comprehensive dataset synthesized from several public network traffic benchmarks. Experimental results show FlowGraphNet significantly outperforms state-of-the-art methods, achieving 99.89% accuracy in distinguishing malicious from benign traffic. Our primary contribution is the synergistic integration of CNN-based image feature learning and GNN-based session-level relational modeling. This combined approach enhances the detection of sophisticated and coordinated cyberattacks, offering a promising new direction for cybersecurity defenses.