  Recent experiments on the Iron-based superconductor FeSe in a high magnetic
field have suggested the presence of both the fluctuation-induced vortex liquid
regime and a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice. To get a
general picture on the magnetic phase diagram in type II superconductors with
strong superconducting (SC) fluctuation and strong paramagnetic pair-breaking
(PPB) such as FeSe, the vortex lattice melting curve Hm(T) is theoretically
investigated in the situations where a FFLO state is expected to occur. In
general, the PPB tends to narrow the vortex liquid regime intervening between
Hc2(T) and Hm(T). In particular, the vortex liquid regime is found to rapidly
shrink upon entering, by cooling, the temperature range in which the FFLO state
with a periodic modulation parallel to the magnetic field is stable in the mean
field theory. Based on the present results, the high field SC phase diagrams of
FeSe in the parallel and perpendicular field configurations are discussed.
