The photoproduction of heavy vector mesons in the electromagnetic interactions of ultra-relativistic nuclei is thought to be sensitive to the gluon distributions in the nucleus and thus to cold nuclear effects like shadowing or gluon saturation. Besides the well known observations of vector meson production in ultra-peripheral collisions, first observations of an excess over the expected hadronic J/$\psi$ production at very low transverse momentum ($p_T < $0.3 GeV/$c$) in peripheral and semi-central nucleus-nucleus collisions both at LHC and RHIC energies were interpreted as the first sign of coherent J/$\psi$ photoproduction occurring in Pb-Pb collisions with nuclear overlap. The ALICE Collaboration published the J/$\psi$ coherent photoproduction cross sections in peripheral and semi-central Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV and forward rapidity ($2.5<y<4.0$). Using the LHC Run-2 data, ALICE presents preliminary results in peripheral Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV at mid-rapidity ($|y|<0.9$) and forward rapidity. Thanks to the very good tracking resolution of the central barrel, the extraction of the $p_T$-differential cross section was also possible, strengthening the photoproduction origin of the observed J/$\psi$ excess. The quantitative understanding of this low-$p_T$ excess poses significant theoretical challenges since the J/$\psi$ photoproduction depends on the collision dynamics as well as on the photon-flux and the photonuclear cross section. In this proceeding, we present the latest ALICE measurements on J/$\psi$ photoproduction cross section in peripheral Pb-Pb collisions, with emphasis on the new forward measurement in the dimuon decay channel at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. These results will be discussed and compared to several model calculations of J/$\psi$ photoproduction in Pb-Pb collisions with nuclear overlap.