Draper has grown into a leading player over the past year, and his real ambition is to land the biggest prize in the sport.
The way the 23-year-old British overcomes Monfils is another example of his maturity.
After two experiences on Paris clay, Draper returns to a place to prove.
Patience is required when he fights against Italian rival Mattia Bellucci on Tuesday to win his first professional victory at Roland Garros.
This is a similar theme for the popular Monfils, who can whip the crowd with his interesting shooting and infectiousness.
French fans are known for their hilarious reputation and play one of his favorite sons in the twilight of his career, creating a vibrant atmosphere that Draper has to block.
Crucially, he remained calm for most of the entertainment competitions.
Despite his mistakes cheering enthusiastically, the audience begged to stop yelling, but Draper stayed to regain the lead after Monfils upgraded.
However, the signs of stirring do show the fourth group.
