The invention relates to a process for FCC pretreatment by mild hydrocracking of a hydrocarbon feedstock that comprises a vacuum distillate fraction or a deasphalted oil or else a mixture of these two fractions, said primary feedstock, to produce gas oil and an effluent having an initial boiling point of more than 320° C., said effluent (FCC feedstock) then being subjected to a catalytic cracking, process in which at least 85% by weight of said primary feedstock ends above 375° C. and at least 95% by weight of said primary feedstock ends below 650° C., whereby the mild hydrocracking is performed under an absolute pressure of 2 to 12 MPa and at a temperature of between 300 and 500° C., characterized in that the hydrocarbon feedstock also comprises a lighter hydrocarbon fraction, a so-called secondary feedstock, of which at least 50% by weight ends below 375° C. and at least 80% ends above 200° C.