  The first measurement of the polarisation of coherently photoproduced
J/$\psi$ mesons in ultra-peripheral Pb$-$Pb collisions, using data at
$\sqrt{s_{\rm NN}}=5.02$ TeV, is presented. The J/$\psi$ meson is measured via
its dimuon decay channel in the forward rapidity interval $-4.0 < y < -2.5$
using the ALICE detector at the CERN LHC. An event sample corresponding to an
integrated luminosity of 750 $\mu{\rm b}^{-1}$ $\pm$ 5% (syst) is analysed.
Hadronic activity is highly suppressed since the interaction is mediated by a
photon. The polar and azimuthal angle distributions of the decay muons are
measured, and the polarisation parameters $\mathbf{\lambda_{\theta}}$,
$\mathbf{\lambda_{\varphi}}$, $\mathbf{\lambda_{\theta\varphi}}$ are extracted.
The analysis is carried out in the helicity frame. The results are found to be
consistent with a transversely polarised J/$\psi$. These values are compared
with previous measurements by the H1 and ZEUS experiments. The polarisation
parameters of coherent J/$\psi$ photoproduction in Pb$-$Pb collisions are found
to be consistent with the $s$-channel helicity conservation hypothesis.
