Process for producing middle distillates from a paraffinic feedstock produced by Fischer-Tropsch synthesis comprising a content of n-paraffins of greater than 70% by weight relative to the total mass of said feedstock, a content of oxygen-comprising products of less than 10% by weight, a content of unsaturated substances of less than 20% by weight and a content of isoparaffins of less than 10% by weight, relative to the total mass of said feedstock, comprising at least: a) a step of hydrotreatment of said feedstock in the presence of hydrogen and a hydrotreatment catalyst at a temperature of between 100 and 450°C, at a pressure of between 0.5 and 15 MPa, the hydrogen being introduced into said hydrotreatment step at a flow rate such that the hydrogen/feedstock ratio by volume is between 50 and 10 000 normal litres per litre, and at a hourly space velocity of between 0.1 and 10 h -1, the hydrotreatment catalyst comprising palladium on alumina, b) a step of separation of at least a portion of the effluent resulting from step a) into at least one light fraction, at least one liquid hydrocarbon effluent and at least one liquid effluent comprising water, c) a step of hydroisomerization/hydrocracking of at least a portion of the liquid hydrocarbon effluent resulting from step b), at a temperature of between 200 and 450°C, at a pressure of between 0.2 and 15 MPa, at a space velocity of between 0.1 h -1 and 10 h -1 and at a hydrogen content of between 100 and 2000 normal litres of hydrogen per litre of feedstock and per hour, in the presence of a hydroisomerization/hydrocracking catalyst and a stream of hydrogen comprising a content of atomic oxygen, expressed in parts per million by volume (ppmv), of less than 500 ppmv, d) a step of fractionation of the effluent resulting from step c) to obtain at least one middle distillate fraction, the hydroisomerization/hydrocracking catalyst comprising at least one noble metal from group VIII, said noble metal being platinum active in its reduced form, the content of noble metal in said catalyst being between 0.10 and 2% by weight relative to the finished catalyst, and at least one solid Brønsted acid consisting of silica-alumina, wherein said stream of hydrogen of step c) undergoes a step of purification before being introduced into said step c) in order to limit the content of molecules containing at least one oxygen atom in said stream, in the case where said stream contains a content of atomic oxygen of greater than 500 ppm by volume. a) a step of hydrotreatment of said feedstock in the presence of hydrogen and a hydrotreatment catalyst at a temperature of between 100 and 450°C, at a pressure of between 0.5 and 15 MPa, the hydrogen being introduced into said hydrotreatment step at a flow rate such that the hydrogen/feedstock ratio by volume is between 50 and 10 000 normal litres per litre, and at a hourly space velocity of between 0.1 and 10 h -1, the hydrotreatment catalyst comprising palladium on alumina, b) a step of separation of at least a portion of the effluent resulting from step a) into at least one light fraction, at least one liquid hydrocarbon effluent and at least one liquid effluent comprising water, c) a step of hydroisomerization/hydrocracking of at least a portion of the liquid hydrocarbon effluent resulting from step b), at a temperature of between 200 and 450°C, at a pressure of between 0.2 and 15 MPa, at a space velocity of between 0.1 h -1 and 10 h -1 and at a hydrogen content of between 100 and 2000 normal litres of hydrogen per litre of feedstock and per hour, in the presence of a hydroisomerization/hydrocracking catalyst and a stream of hydrogen comprising a content of atomic oxygen, expressed in parts per million by volume (ppmv), of less than 500 ppmv, d) a step of fractionation of the effluent resulting from step c) to obtain at least one middle distillate fraction, the hydroisomerization/hydrocracking catalyst comprising at least one noble metal from group VIII, said noble metal being platinum active in its reduced form, the content of noble metal in said catalyst being between 0.10 and 2% by weight relative to the finished catalyst, and at least one solid Brønsted acid consisting of silica-alumina,