We use Very Large Telescope (VLT)/Fibre Large Array Multi Element Spectrograph (FLAMES) intermediate-resolution (R similar to 6500) spectra of individual red giant branch stars in the near-infrared Ca ii triplet (CaT) region to investigate the wide-area metallicity properties and internal kinematics of the Sextans dwarf spheroidal galaxy (dSph). Our final sample consists of 174 probable members of Sextans with accurate line-of-sight velocities (+/- 2 km s-1) and CaT [Fe/H] measurements (+/- 0.2 dex). We use the Mg i line at 8806.8 A as an empirical discriminator for distinguishing between probable members of the dSph (giant stars) and probable Galactic contaminants (dwarf stars). Sextans shows a similar chemodynamical behaviour to other Milky Way dSphs, with its central regions being more metal rich than the outer parts and with the more metal-rich stars displaying colder kinematics than the more metal-poor stars. Hints of a velocity gradient are found along the projected major axis and along an axis at position angle (PA) = 191 degrees, however, a larger and more spatially extended sample may be necessary to pin down the amplitude and direction of this gradient. We detect a cold kinematic substructure at the centre of Sextans, consistent with being the remnant of a disrupted very metal poor stellar cluster. We derive the most extended line-of-sight velocity dispersion profile for Sextans, out to a projected radius of 16. From Jeans modelling of the observed line-of-sight velocity dispersion profile we find that this is consistent with both a cored dark matter halo with large core radius and cuspy halo with low concentration. The mass within the last measured point is in the range 2-4 x 108 M-circle dot, giving very large mass-to-light ratios, from 460 to 920 (M/L)(V, circle dot).