We demonstrate for the first time plasmonic nanotweezers based on Au bowtie nanoantenna arrays (BNAs) that utilize a femtosecond-pulsed input source to enhance trapping of both Rayleigh and Mie particles. Using ultra-low input power densities, we demonstrate that the high-peak powers associated with a femtosecond source augment the trap stiffness to 2x that of nanotweezers employing a continuous-wave source, and 5x that of conventional tweezers using a femtosecond source. We show that for trapped fluorescent microparticles the two-photon response is enhanced by 2x in comparison to the response without nanoantennas. We also demonstrate tweezing of 80-nm diameter Ag nanoparticles, and observe an enhancement of the second-harmonic signal of ~3.5x for the combined nanoparticle-BNA system compared to the bare BNAs. Finally, under select illumination conditions, fusing of Ag nanoparticles to the BNAs is observed which holds potential for in situ fabrication of three-dimensional, bimetallic nanoantennas.