The Belarusian, last year's losing finalist, was made to work hard for about an hour, with the local hero delighting home fans with several spectacular winners.
"That was a very tough opponent. Tricky match. I'm happy that I closed it in straight sets," Sabalenka said.
"She played really incredible tennis and forced me to step in and play on another level. I am happy I could handle it and win."
The world number one earned an early break with a powerful forehand to go 3-1 up but Jacquemot broke straight back.
On a day when the men's world number one Jannik Sinner crashed out in five sets to Juan Manuel Cerundolo, Sabalenka had to dig deep in the first set against the world number 67.
She had set point at 5-4 on Jacquemot's serve but the French player, who had the crowd on their feet at times, managed to match Sabalenka's power with superb precision and level.
The top seed kept her composure and won the first set on her third set point, and she never looked back.
She grabbed a break at the start of the second set and raced to a 3-0 lead, giving Jacquemot, who was quickly running out of steam, no chance of a comeback.
"It's always challenging playing her," the top seed said. "She's a fighter. She's putting all of the balls back. You have to really work for each point, especially on the clay court."
A four-time Grand Slam champion, Sabalenka is still looking to land her first French Open title.
She will next face Australia's Daria Kasatkina.