  Photonuclear reactions are induced by the strong electromagnetic field
generated by ultrarelativistic heavy ions. These processes have been
extensively studied in ultraperipheral collisions. In recent years, the
observation of coherent J/$\psi$ photoproduction has been claimed in
nucleus-nucleus (A-A) collisions with nuclear overlap, based on the measurement
of an excess in the very low transverse momentum ($p_{\rm T}$) J/$\psi$ yield.
Such quarkonium measurements can help constraining the nuclear gluon
distribution at low Bjorken-$x$ and can shed light on the theory behind photon
induced reactions in A-A collisions with nuclear overlap. In order to confirm
the photoproduction origin of the very low-$p_{\rm T}$ J/$\psi$ yield excess,
polarization measurement is a golden observable. It is indeed expected that the
produced quarkonium would keep the polarization of the incoming photon due to
$s$-channel helicity conservation. ALICE can measure inclusive and exclusive
quarkonium production down to zero transverse momentum, at forward rapidity
(2.5 $< y <$ 4) and midrapidity ($|y| <$ 0.9). In this contribution, we will
report on the new preliminary measurement of the $y$-differential cross section
and the first polarization analysis at LHC of coherently photoproduced J/$\psi$
in peripheral Pb-Pb collisions. Both measurements are conducted at forward
rapidity in the dimuon decay channel.
