Text-guided image editing, a pivotal task in modern multimedia content creation, has seen remarkable progress with training-free methods that eliminate the need for additional optimization. Despite recent progress, existing methods are typically constrained by a competitive paradigm in which the editing and reconstruction branches are independently driven by their respective objectives to maximize alignment with target and source prompts. The adversarial strategy causes semantic conflicts and unpredictable outcomes due to the lack of coordination between branches. To overcome these issues, we propose Coopetitive Training-Free Image Editing (CoEdit), a novel zero-shot framework that transforms attention control from competition to coopetitive negotiation, achieving editing harmony across spatial and temporal dimensions. Spatially, CoEdit introduces Dual-Entropy Attention Manipulation, which quantifies directional entropic interactions between branches to reformulate attention control as a harmony-maximization problem, eventually improving the localization of editable and preservable regions. Temporally, we present Entropic Latent Refinement mechanism to dynamically adjust latent representations over time, minimizing accumulated editing errors and ensuring consistent semantic transitions throughout the denoising trajectory. Additionally, we propose the Fidelity-Constrained Editing Score, a composite metric that jointly evaluates semantic editing and background fidelity. Extensive experiments on standard benchmarks demonstrate that CoEdit achieves superior performance in both editing quality and structural preservation, enhancing multimedia information utilization by enabling more effective interaction between visual and textual modalities. The code will be available at https://github.com/JinhaoShen/CoEdit.