The demand for a quick response from cloud services is rapidly increasing day-by-day. Fog computing is a trending solution to fulfil the demands. When integrated with the cloud, this technology can tremendously improve the performance. Like any other technology, Fog also has the shortcoming of limited resources. The difficulty of efficient scheduling of tasks among limited resources to minimize makespan and energy consumption, while still guaranteeing appropriate execution cost, continues to be a significant issue for research. Hence, this study introduces a Differential Evolution-Grey Wolf Optimization (DE-GWO) technique to enhance the scheduling of scientific workflows under cloud-fog settings. The objective of the proposed DE-GWO algorithm is to mitigate the issue of slow convergence and low accuracy that is often seen in the classical GWO algorithm. The DE method is chosen as the evolutionary pattern of wolves to speed up convergence and enhance GWO's accuracy. This study further formulates a weighted sum based objective function which incorporates three criteria, namely makespan, cost and energy consumption. In this study, the DE-GWO technique is evaluated and compared with many conventional and hybrid optimization algorithms. The simulations use five scientific workflows datasets which includes Montage, Cybershake, Epigenomics, LIGO and SIPHT. The DE-GWO algorithm demonstrates superior performance compared to all conventional algorithms across several scientific workflows and performance criteria. The methodology has a commendable level of competitiveness when compared to other methods, since DE incorporates evolution and elimination mechanisms in GWO and GWO retains a good balance between exploration and exploitation.