  Direct imaging has led to the discovery of several giant planet and brown
dwarf companions. These imaged companions populate a mass, separation and age
domain (mass>1MJup, orbits>5AU, age<1Gyr) quite distinct from the one occupied
by exoplanets discovered by the radial velocity or transit methods. This
distinction could pinpoint that different formation mechanisms are at play. We
aim at investigating correlations between the host star's mass and the presence
of wide-orbit giant planets, and at providing new observational constraints on
planetary formation models. We observed 58 young and nearby M-type dwarfs in
L'-band with the VLT/NaCo instrument and used ADI algorithms to optimize the
sensitivity to planetary-mass companions and to derive the best detection
limits. We estimate the probability of detecting a planet as a function of its
mass and physical separation around each target. We conduct a Bayesian analysis
to determine the frequency of substellar companions orbiting low-mass stars,
using a homogenous sub-sample of 54 stars. We derive a frequency of
$4.4^{+3.2}_{-1.3}\%$ for companions with masses in the range of 2-80MJup}, and
$2.3^{+2.9}_{-0.7}$\% for planetary mass companions (2-14MJup), at physical
separations of 8 to 400AU for both cases. Comparing our results with a previous
survey targeting more massive stars, we find evidence that substellar
companions more massive than 1MJup with a low mass ratio Q with respect to
their host star (Q<1%), are less frequent around low-mass stars. This may
represent an observational evidence that the frequency of imaged wide-orbit
substellar companions is correlated with stellar mass, corroborating
theoretical expectations. On the opposite, we show statistical evidence that
intermediate-mass ratio (1%<Q<5%) companion with masses >2MJup might be
independent from the mass of the host star.
