In this study, we performed high-magnetic-field magnetization, dielectric, and ultrasound measurements on an organic salt showing a ferroelectric spin-Peierls (FSP) state, which is in close proximity to a quantum critical point. In contrast to the sparsely distributed gas-like spin solitons typically observed in conventional spin-Peierls (SP) states, the FSP state exhibits dense liquid-like spin solitons resulting from strong quantum fluctuations, even at low fields. Nevertheless, akin to conventional SP systems, a magnetic-field-induced transition is observed in the FSP state. In conventional high-field SP states, an emergent wave vector results in the formation of a spin-soliton lattice. However, in the present high-field FSP state, the strong quantum fluctuations preclude the formation of such a soliton lattice, causing the dense solitons to remain in a quantum-mechanically melted state. This observation implies the realization of a quantum liquid--liquid transition of topological particles carrying spin and charge in a ferroelectric insulator.