Process for the production of a hydrocarbon fraction with a high octane number and a low sulfur content from a hydrocarbon feedstock, comprising at least the following stages: 1) a hydrodesulfurization stage of the hydrocarbon feedstock, and 2) at least one stage for extracting aromatic compounds on all or part of the effluent that is obtained from the hydrodesulfurization stage, whereby said extraction leads to a paraffin-enriched raffinate and an aromatic compound-enriched extract sent to a gasoline pool to improve its octane number, wherein a portion of the paraffinic raffinate can be used in a mixture with the aromatic extract; another portion can be used as a petrochemistry base either for producing aromatic compounds or for producing olefins.