The globular cluster (GC) systems of low-mass late-type galaxies, such as NGC 2403, have been poorly studied to date. As a low mass galaxy (M* = 7 × 109 M⊙), cosmological simulations predict NGC 2403 to contain few, if any, accreted GCs. It is also isolated, with a remarkably undisturbed HI disc. Based on candidates from the literature, Sloan Digital Sky Survey and Hyper Suprime-Cam imaging, we selected several GCs for follow-up spectroscopy using the Keck Cosmic Web Imager. From their radial velocities and other properties, we identify eight bona-fide GCs associated with either the inner halo or the disc of this bulgeless galaxy. A stellar population analysis suggests a wide range of GC ages from shortly after the big bang until the present day. We find all of the old GCs to be metal-poor with [Fe/H] ≤ -1. The age-metallicity relation for the observed GCs suggests that they were formed over many Gyr from gas with a low effective yield, similar to that observed in the SMC. Outflows of enriched material may have contributed to the low yield. With a total system of ~50 GCs expected, our study is the first step in fully mapping the star cluster history of NGC 2403 in both space and time.