Tunisia's Jabeur has struggled to build momentum during an injury-hit season and her preparation for the grass-court major was far from ideal with early losses in Berlin and Eastbourne, but the sixth seed showed her calibre against Frech.
After narrowly missing the opportunity to break the 70th-ranked Frech early on with two wayward drop shots, Jabeur got her nose in front in the fifth game thanks to clean hitting and raced through the opening set.
"I always feel so great to come back here. Last year I had an amazing run and hopefully this year it will be a little bit better," said Jabeur, who lost to Elena Rybakina in last year's final.
"I walked into the locker room and there was Elena's photo with the trophy so that didn't help at all," she joked.
"But it's amazing to come back here, just the atmosphere, the grass is so beautiful and I love connecting with nature."
After narrowly missing the opportunity to break the 70th-ranked Frech early with two wayward drop shots, Jabeur got her nose in front in the fifth game thanks to clean hitting and she raced through the opening set.
The 28-year-old moved with ease and displayed a stunning range of shots that included drops, lobs and scoops to overwhelm Frech and go 3-1 up in the next set.
Frech grabbed a break against the run of play before drawing level but Jabeur, who needed three sets to overcome the 25-year-old at Indian Wells this year, ensured there would be no late drama under the Court One roof.
Jabeur restored her advantage as Frech sent a shot long and closed out the contest on serve to set up a meeting with either unseeded Belgian Ysaline Bonaventure or Chinese qualifier Bai Zhuoxuan.
"I'm just trying to enjoy my time, enjoy playing tennis, doing some cool drop shots and see what's going to happen," said Jabeur, who hit 33 winners but also made 29 unforced errors with her high-risk style.
"It reflects my character. I like to joke around a bit," she said. "I hate routine... I like to entertain the crowd with cool shots, so maybe I'll keep doing that."
