The Leo group elliptical NGC 3379 is one of the few normal elliptical galaxies close enough to make possible observations of resolved stellar populations, deep globular cluster (GC) photometry and high signal-to-noise ratio GC spectra. We have obtained Gemini/GMOS spectra for 22 GCs associated with NGC 3379. We derive ages, metallicities and α-element abundance ratios from simple stellar population models using the recent multi-index χ2 minimization method of Proctor & Sansom. All of these GCs are found to be consistent with old ages, i.e. >~10Gyr, with a wide range of metallicities. This is comparable to the ages and metallicities that Gregg et al. found a couple of years ago for resolved stellar populations in the outer regions of this elliptical. A trend of decreasing α-element abundance ratio with increasing metallicity is indicated. The projected velocity dispersion of the GC system is consistent with being constant with radius. Non-parametric, isotropic models require a significant increase in the mass-to-light ratio at large radii. This result is in contrast to that of Romanowsky et al., who recently found a decrease in the velocity dispersion profile as determined from planetary nebulae (PN). Our constant dispersion requires a normal-sized dark halo, although without anisotropic models we cannot rigorously determine the dark halo mass. A two-sided χ2 test over all radii gives a 2σ difference between the mass profile derived from our GCs compared to the PN-derived mass model of Romanowsky et al. However, if we restrict our analysis to radii beyond one effective radius and test if the GC velocity dispersion is consistently higher, we determine a > 3σ difference between the mass models, and hence we favour the conclusion that NGC 3379 does indeed have dark matter at large radii in its halo.