Supply chain carbon emissions account for over 80% of greenhouse gas output in most consumer industries, yet the operational link between demand forecasting accuracy and downstream environmental impact remains poorly quantified. Here we propose CGAN-MCDFN, an integrated framework coupling an explainable deep learning demand predictor with a simulation-based carbon emission model aligned with the Greenhouse Gas Protocol Scope 3 standard. The framework incorporates Conditional Generative Adversarial Network augmentation for sparse product demand, multi-channel encoding for heterogeneous signal fusion, and per-prediction SHAP-based explanations. Experiments on the M5 and Rossmann retail benchmarks yield rootmean- square-error improvements of 22.7% and 19.4% over the strongest baselines (both p < 0.001). Translating these accuracy gains through a carbon simulation calibrated with Ecoinvent 3.9 emission factors, we estimate a 32.5% scenario-level reduction in overstock-related CO2e emissions relative to an XGBoost baseline, with sensitivity analysis confirming that relative model rankings are preserved under ±30% emission-factor variation. SHAP analysis reveals that a carbon-index sustainability covariate ranks fourth among 47 predictors, and its importance increases at longer forecast horizons. We acknowledge that the carbon estimates are simulation-based and propose a three-stage validation roadmap for transitioning to auditable life-cycle-assessment data. Code and augmented datasets will be released upon acceptance.