  UNIONS is an ongoing deep photometric multi-band survey of the Northern sky.
As part of UNIONS, CFIS provides r-band data which we use to study weak-lensing
peak counts for cosmological inference. We assess systematic effects for
weak-lensing peak counts and their impact on cosmological parameters for the
UNIONS survey. In particular, we present results on local calibration,
metacalibration shear bias, baryonic feedback, the source galaxy redshift
estimate, intrinsic alignment, and the cluster member dilution. For each
uncertainty and systematic effect, we describe our mitigation scheme and the
impact on cosmological parameter constraints. We obtain constraints on
cosmological parameters from MCMC using CFIS data and MassiveNuS N-body
simulations as a model for peak counts statistics. Depending on the calibration
(local versus global, and the inclusion of the residual multiplicative shear
bias), the mean matter density parameter $\Omega_m$ can shift up to $-0.024$
($-0.5\sigma$). We also see that including baryonic corrections can shift
$\Omega_m$ by $+0.027$ ($+0.5 \sigma$) with respect to the DM-only simulations.
Reducing the impact of the intrinsic alignment and cluster member dilution
through signal-to-noise cuts can lead to a shift in $\Omega_m$ of $+0.027$
($+0.5 \sigma$). Finally, with a mean redshift uncertainty of $\Delta \bar{z} =
0.03$, we see that the shift of $\Omega_m$ ($+0.001$ which corresponds to
$+0.02 \sigma$) is not significant. This paper investigates for the first time
with UNIONS weak-lensing data and peak counts the impact of systematic effects.
The value of $\Omega_m$ is the most impacted and can shift up to $\sim 0.03$
which corresponds to $0.5\sigma$ depending on the choices for each systematics.
We expect constraints to become more reliable with future (larger) data
catalogues, for which the current pipeline will provide a starting point.
