Method for converting feedstocks comprising a hydrotreatment step, a hydrocracking step, a precipitation step and a sediment separation step, in order to produce fuel oils

The invention concerns a process for the treatment of a hydrocarbon feed, said process comprising the following steps: a) a hydrotreatment step, in which the hydrocarbon feed and hydrogen are brought into contact over a hydrotreatment catalyst, b) an optional step of separating the effluent obtained from the hydrotreatment step a), c) a step of hydrocracking at least a portion of the effluent obtained from step a) or at least a portion of the heavy fraction obtained from step b), d) a step of separating the effluent obtained from step c), e) a step of precipitating sediments, f) a step of physical separation of the sediments from the heavy liquid fraction obtained from step e), g) a step of recovering a liquid hydrocarbon fraction having a sediment content, measured using the ISO 10307-2 method, of 0.1% by weight or less.