  We report the discovery and characterisation of a super-Earth and a
sub-Neptune transiting the bright ($K=8.8$), quiet, and nearby (37 pc) M3V
dwarf TOI-1266. We validate the planetary nature of TOI-1266 b and c using four
sectors of TESS photometry and data from the newly-commissioned 1-m SAINT-EX
telescope located in San Pedro M\'artir (Mexico). We also include additional
ground-based follow-up photometry as well as high-resolution spectroscopy and
high-angular imaging observations. The inner, larger planet has a radius of
$R=2.37_{-0.12}^{+0.16}$ R$_{\oplus}$ and an orbital period of 10.9 days. The
outer, smaller planet has a radius of $R=1.56_{-0.13}^{+0.15}$ R$_{\oplus}$ on
an 18.8-day orbit. The data are found to be consistent with circular, co-planar
and stable orbits that are weakly influenced by the 2:1 mean motion resonance.
Our TTV analysis of the combined dataset enables model-independent constraints
on the masses and eccentricities of the planets. We find planetary masses of
$M_\mathrm{p}$ = $13.5_{-9.0}^{+11.0}$ $\mathrm{M_{\oplus}}$ ($<36.8$
$\mathrm{M_{\oplus}}$ at 2-$\sigma$) for TOI-1266 b and $2.2_{-1.5}^{+2.0}$
$\mathrm{M_{\oplus}}$ ($<5.7$ $\mathrm{M_{\oplus}}$ at 2-$\sigma$) for TOI-1266
c. We find small but non-zero orbital eccentricities of $0.09_{-0.05}^{+0.06}$
($<0.21$ at 2-$\sigma$) for TOI-1266 b and $0.04\pm0.03$ ($<0.10$ at
2-$\sigma$) for TOI-1266 c. The equilibrium temperatures of both planets are of
$413\pm20$ K and $344\pm16$ K, respectively, assuming a null Bond albedo and
uniform heat redistribution from the day-side to the night-side hemisphere. The
host brightness and negligible activity combined with the planetary system
architecture and favourable planet-to-star radii ratios makes TOI-1266 an
exquisite system for a detailed characterisation.
