We have obtained Gemini/GMOS spectra for 22 GCs associated with NGC 3379. We derive ages, metallicities and alpha-element abundance ratios from simple stellar population models using the multi-index chi^2 minimisation method of Proctor & Sansom (2002). All of these GCs are found to be consistent with old ages, i.e. >10 Gyr, with a wide range of metallicities. A trend of decreasing alpha-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. (2003) who find a decrease in the velocity dispersion profile as determined from planetary nebulae. Our constant dispersion requires a normal sized dark halo, although without anisotropic models we cannot rigorously determine the dark halo mass. A two-sided chi^2 test over all radii, gives a 2 sigma difference between the mass profile derived from our GCs compared to the PN-derived mass model of Romanowsky et al. (2003). 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 >3 sigma difference between the mass models, and hence favor the conclusion that NGC 3379 does indeed have dark matter at large radii in its halo. (abridged)