Photonuclear reactions are induced by the strong electromagnetic field generated by ultrarelativistic heavy-ion collisions. These processes have been extensively studied in ultraperipheral collisions, in which the impact parameter is larger than twice the nuclear radius. 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 (with respect to hadroproduction expectations) in the yield of very low transverse momentum ($p_\mathrm{T}$) J/$\psi$. Such quarkonium measurements can help constraining the nuclear gluon distributions at low Bjorken-$x$ and high energy. In addition, they can shed light on the theory behind photon induced reactions in A--A collisions with nuclear overlap, including possible interactions of the measured probes with the formed and fast expanding quark-gluon plasma. In order to confirm the photoproduction origin of the very low $p_{T}$ 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. Comparison with models will be shown when available.