Process for the treatment of petroleum-based feedstocks, at least 80% by weight of which boils above 340°C and which comprise at least 0.05% by weight of sulfur, said petroleum-based feedstocks being chosen from the group formed by straight-run vacuum distillates, vacuum distillates resulting from a conversion process, deasphalted oils or residues resulting from processes for the conversion of heavy feedstocks, taken alone or as a mixture, in order to produce at least one gas oil cut with a sulfur content of at most 10 ppm by weight, said process comprising the following stages: a) mild hydrocracking in a fixed bed of at least one catalyst comprising from 0.5 to 10% by weight of nickel oxide and from 1 to 30% by weight of molybdenum oxide, on an amorphous inorganic support, at a temperature of between 350 and 450°C, a pressure of between 2.5 MPa and 7 MPa, an hourly space velocity of between 0.2 h -1 and 5 h -1 and in the presence of 200 to 1500 Sm 3 of hydrogen/m 3 of feedstock, such that the net conversion to products boiling below 360°C is between 15 and 45% by weight, b) separation, from the effluent resulting from stage a), of a gas comprising hydrogen, of the hydrogen sulphide formed in stage a), of at least one distillate cut including a gas oil fraction and of a fraction which is heavier than gas oil, c) hydrotreatment, by contact with at least one catalyst, of at least a portion of said distillate cut obtained in stage b) including the gas oil fraction, as a mixture with a feedstock resulting from a crude or refined renewable source, said feedstock resulting from a renewable source comprising oils and/or fats of vegetable and/or animal and/or fish origin and products derived from these sources, said oils and/or fats being crude or having been subjected beforehand to a refining treatment, and also mixtures of feedstocks of such origins, said feedstocks being composed of chemical structures of the type of triglycerides and/or fatty acids, the proportions of the mixture formed of the feedstock resulting from a renewable source and of the distillate cut including a gas oil fraction being 1 to 75% by volume of feedstock resulting from a renewable source and 99% to 25% by volume of the distillate cut including a gas oil fraction, said stage c) being carried out at a temperature of between 180 and 310°C, a pressure of between 2 and 10 MPa, an hourly space velocity of between 0.1 and 10 h -1 and in the presence of 200 to 5000 Sm 3 of hydrogen/m 3 of feedstock, d) separation of the hydrogen, of the gases and of at least one gas oil cut with a sulfur content of at most 10 ppm by weight. a) mild hydrocracking in a fixed bed of at least one catalyst comprising from 0.5 to 10% by weight of nickel oxide and from 1 to 30% by weight of molybdenum oxide, on an amorphous inorganic support, at a temperature of between 350 and 450°C, a pressure of between 2.5 MPa and 7 MPa, an hourly space velocity of between 0.2 h -1 and 5 h -1 and in the presence of 200 to 1500 Sm 3 of hydrogen/m 3 of feedstock, such that the net conversion to products boiling below 360°C is between 15 and 45% by weight, b) separation, from the effluent resulting from stage a), of a gas comprising hydrogen, of the hydrogen sulphide formed in stage a), of at least one distillate cut including a gas oil fraction and of a fraction which is heavier than gas oil, c) hydrotreatment, by contact with at least one catalyst, of at least a portion of said distillate cut obtained in stage b) including the gas oil fraction, as a mixture with a feedstock resulting from a crude or refined renewable source, said feedstock resulting from a renewable source comprising oils and/or fats of vegetable and/or animal and/or fish origin and products derived from these sources, said oils and/or fats being crude or having been subjected beforehand to a refining treatment, and also mixtures of feedstocks of such origins, said feedstocks being composed of chemical structures of the type of triglycerides and/or fatty acids, the proportions of the mixture formed of the feedstock resulting from a renewable source and of the distillate cut including a gas oil fraction being 1 to 75% by volume of feedstock resulting from a renewable source and 99% to 25% by volume of the distillate cut including a gas oil fraction, said stage c) being carried out at a temperature of between 180 and 310°C, a pressure of between 2 and 10 MPa, an hourly space velocity of between 0.1 and 10 h -1 and in the presence of 200 to 5000 Sm 3 of hydrogen/m 3 of feedstock, d) separation of the hydrogen, of the gases and of at least one gas oil cut with a sulfur content of at most 10 ppm by weight.