All three of former world number one Kuerten's Grand Slam triumphs came at the French Open (1997, 2000 and 2001), and 18-year-old Fonseca said that he had made the tournament more popular with Brazilian tennis fans.
"I knew there were going to be a lot of Brazilians here in Paris, a lot of Brazilians living here, and they come a lot," Fonseca told reporters after his win over 30th seed Hurkacz on Tuesday.
"I think because of Guga (Kuerten), because of the tradition, there are a lot of Brazilians."
One of the rising stars of the men's tour, Fonseca shocked ninth seed Andrey Rublev on his Grand Slam main draw debut at the Australian Open in January and became the youngest Brazilian to win an ATP tournament at the Argentina Open the following month.
Fonseca said he wanted to focus on improving himself instead of the growing pressure brought on by rising expectations.
"Sometimes the pressure is going to come. It's normal. You need to deal with it," he added.
Fonseca may not enjoy the same level of support in the next round on Thursday as he faces Frenchman Pierre-Hugues Herbert.