We present a detailed study of the faint Milky Way satellite Draco II (Dra II) from deep CFHT/MegaCam broad-band g and i photometry and narrow-band metallicity-sensitive CaHK observations, along with follow-up Keck II/DEIMOS multi-object spectroscopy. Forward modelling of the deep photometry allows us to refine the structural and photometric properties of Dra II: the distribution of stars in colour-magnitude space implies Dra II is old (13.5 ± 0.5 Gyr), very metal-poor, very faint (L_V = 180 ^{+124}_{-72} { L_⊙}), and at a distance d = 21.5 ± 0.4 { kpc}. The narrow-band, metallicity-sensitive CaHK Pristine photometry confirms this very low metallicity ([Fe/H] = -2.7 ± 0.1 dex). Even though our study benefits from a doubling of the spectroscopic sample size compared to previous investigations, the velocity dispersion of the system is still only marginally resolved (σ _{vr}< 5.9 { km s^{-1}} at the 95 per cent confidence level) and confirms that Dra II is a dynamically cold stellar system with a large recessional velocity (< vr> = -342.5^{+1.1}_{-1.2}{ km s^{-1}}). We further show that the spectroscopically confirmed members of Dra II have a mean proper motion of (μ _α ^*,μ _δ)=(1.26 ± 0.27,0.94 ± 0.28) { mas/yr} in the Gaia DR2 data, which translates to an orbit with a pericentre and an apocentre of 21.3 ^{+0.7}_{-1.0} and 153.8 ^{+56.7}_{-34.7} { kpc}, respectively. Taken altogether, these properties favour the scenario of Dra II being a potentially disrupting dwarf galaxy. The low-significance extra-tidal features we map around the satellite tentatively support this scenario.