We present wide-field spectroscopy of globular clusters around the Leo I group galaxies NGC~3379 and NGC~3384 using the FLAMES multi-fibre instrument at the VLT . We obtain accurate radial velocities for 42 globular clusters ( GCs ) in total , 30 for GCs around the elliptical NGC 3379 , eight around the lenticular NGC 3384 , and four which may be associated with either galaxy . These data are notable for their large radial range extending from 0 \aas@@fstack { \prime } 7 to 14 \aas@@fstack { \prime } 5 ( 2 to 42 kpc ) from the centre of NGC 3379 , and small velocity uncertainties of about 10 km s ^ { -1 } . We combine our sample of 30 radial velocities for globular clusters around NGC 3379 with 8 additional GC velocities from the literature , and find a projected velocity dispersion of \sigma _ { p } = 175 ^ { +24 } _ { -22 } km s ^ { -1 } at R < 5 ^ { \prime } and \sigma _ { p } = 147 ^ { +44 } _ { -39 } at R > 5 ^ { \prime } . These velocity dispersions are consistent with a dark matter halo around NGC 3379 with a concentration in the range expected from a \Lambda CDM cosmological model and a total mass of \approx 6 \times 10 ^ { 11 } M _ { \odot } . Such a model is also consistent with the stellar velocity dispersion at small radii and the rotation of the H i ring at large radii , and has a ( M / L ) _ { \varB } that increases by a factor of five from several kpc to 100 kpc . Our velocity dispersion for the globular cluster system of NGC 3379 is somewhat higher than that found for the planetary nebulae ( PNe ) in the inner region covered by the PN data , and we discuss possible reasons for this difference . For NGC 3384 , we find the GC system has a rotation signature broadly similar to that seen in other kinematic probes of this SB0 galaxy . This suggests that significant rotation may not be unusual in the GC systems of disc galaxies .