Double-gate carbon nanotube field effect transistors (DGCNTFETs) are novel devices showing an interesting property allowing to control the p- or n-type behavior during the device operation. This opens up the opportunity for novel design paradigms. Based on a compact physical model of these devices, we demonstrate the benefit of designing field-programmable gate arrays (FPGAs) using fine-grain DG-CNTFET logic blocs rather than traditional look-up tables and coarse-grain DG-CNTFET logic blocs. In particular, we show a reduction by 13% to 48% on average in terms of delay of FPGA benchmarks.