In this paper, a fractional active disturbance rejection control (FADRC) scheme is proposed for remotely operated vehicles (ROVs) to enhance high-precision positioning and docking control in the presence of ocean current disturbances and model uncertainties. The scheme comprises a double closed-loop fractional-order PIλDμ controller (DFOPID) and a model-assisted finite-time sliding-mode extended state observer (MFSESO). Among them, DFOPID effectively compensates for non-matching disturbances, while its fractional-order term enhances the dynamic performance and steady-state accuracy of the system. MFSESO contributes to enhancing the estimation accuracy through the integration of sliding-mode technology and model information, ensuring the finite-time convergence of observation errors. Numerical simulations and pool experiments have shown that the proposed control scheme can effectively resist disturbances and successfully complete high-precision tasks in the absence of an accurate model. This underscores the independence of this control scheme on accurate model data of an operational ROV. Meanwhile, it also has the advantages of a simple structure and easy parameter tuning. The FADRC scheme presented in this paper holds practical significance and can serve as a valuable reference for applications involving ROVs.