The invention relates to a process for the treatment of a hydrocarbon-containing feedstock making it possible to obtain a heavy hydrocarbon-containing fraction having a low sulphur content, said process comprising the following stages: a) a stage of hydrodemetallization in permutable reactors b) a stage of fixed-bed hydrotreatment of the effluent originating from stage a), c) a stage of hydrocracking in permutable reactors of the effluent originating from stage b), d) a stage of separation of the effluent originating from stage c), e) a stage of precipitation of the sediments, f) a stage of physical separation of said sediments from the heavy liquid fraction originating from stage d), g) a stage of recovery of the distillate cut used in stage e).