Nowadays, cloud computing leverages the capability of Internet-of-Things (IoT) applications by providing computing resources as a form of virtual machine (VM) instances. However, the Cloud data center consumes a large amount of energy while transmitting and computing the IoT applications which lead to a high carbon footprint. On the other hand, the Fog nodes provide various cloud services at the edge of the network which can run the IoT applications locally with minimum energy consumption and delay. Due to the limited resource capacity, the Fog nodes are not suitable for processing the resource-intensive IoT applications. To address these challenges, in this paper, we build sustainable infrastructure in Fog-Cloud environment for processing delay-intensive and resource-intensive applications with an optimal task offloading strategy. The proposed offloading strategy uses Firefly algorithm for finding an optimal computing device based on two Quality-of-Service (QoS) parameters such as energy consumption and computational time. The main objectives of this strategy are to minimize the computational time and the energy consumption of the IoT applications with minimum delay. The effect of the control parameters of the Firefly technique is investigated thoroughly. Through comparisons, we show that the proposed method performs better than the existing ones in terms of various performance metrics including computational time, energy consumption, CO2 emission, and Temperature emission.