Along with Draper, Jacob Fearnley and Cameron Norrie have direct entry into the main draw.
Fearnley, 23, will make his French Open debut after a stunning rise over the past year for the former Texas Christian University student.
Ranked 54th in the world after less than a year as a professional, he played his first ATP Tour clay match in April and has won eight of his 13 matches since.
Former world number eight Norrie, by contrast, has dropped down the rankings, but had a welcome run to the Geneva Open semi-finals in the days before Roland Garros.
In doubles, Britain’s Henry Patten and Finn partner Harri Heliovaara are aiming for their third Grand Slam title together in 12 months, having won Wimbledon and the Australian Open.
Two all-British pairs – Julian Cash and Lloyd Glasspool, and Joe Salisbury and Neal Skupski – are also in the draw, alongside Jamie Murray and American Rajeev Ram.
Alfie Hewett and Gordon Reid will compete in the wheelchair singles and doubles, with Andy Lapthorne in the quad singles.
