Fręch, who is ranked world No. 88 by the Women's Tennis Association (WTA), defeated Chinese Shuai Zhang, ranked No 31, 6-1, 6-1 in their first-round women's singles clash in the French capital on Sunday.
Meanwhile, No 14 Hurkacz beat Belgium's David Goffin, ranked No 111, 6-3, 5-7, 6-4, 2-6, 6-4 in their first-round men's singles match.
Poland's 21st-ranked Magda Linette was set to take on Canada's Leylah Fernandez, ranked No 51, later on Sunday.
Iga Świątek, the world No. 1 in women's tennis, is expected to step on the court on Tuesday.
Świątek is looking to win her third straight title at the French Open.
The 2023 French Open Grand Slam tennis tournament runs until June 12.