Routing resources are the major bottlenecks in improving the performance and power consumption of the current FPGAs. Recently reported researches have shown that carbon nanotube field effect transistors (CNFETs) have considerable potentials for improving the delay and power consumption of the modern FPGAs. In this paper, hybrid CNFET-CMOS architecture is presented for FPGAs and then this architecture is evaluated to be used in modern FPGAs. In addition, we have designed and parameterized the CNFET-based FPGA switches and calibrated them for being utilized in FPGAs at 45 nm, 22 nm and 16 nm technology nodes. Simulation results show that the CNFET-based FPGA switches improve the current FPGAs in terms of performance, power consumption and immunity to process and temperature variations. Simulation results and analyses also demonstrate that the performance of the FPGAs is improved about 30%, on average and the average and leakage power consumptions are reduced more than 6% and 98% respectively when the CNFET switches are used instead of MOSFET FPGA switches. Moreover, this technique leads to more than 20.31% smaller area. It is worth mentioning that the advantages of CNFET-based FPGAs are more considerable when the size of FPGAs grows and also when the technology node becomes smaller.