The family wasn't at Roland Garros a year ago, making it the first Grand Slam tournament since 2003 without either Williams. Serena was still working her way back from a series of health scares, including two foot operations and blood clots. Venus revealed in August she'd been diagnosed with an autoimmune disease that causes fatigue.
Now they've returned.
"I'm happy about it. They're happy about it," Price said Friday. "Serena's thanking God that she's able to play at all. And so is Venus, with her illness; it's still there. They're doing the best they can do."
Which tends to be pretty good, of course.
Both have been ranked No. 1. Serena's 13 Grand Slam titles are by far the most among active women; Venus comes next with seven. None of the other entrants in the French Open, which begins Sunday, owns more career Grand Slam match wins than Serena's 211 or Venus' 210.
And it's certainly tough to match Serena's self-confidence on a tennis court.
When it was pointed out to her Friday that five women divvied up the past five Grand Slam titles -- Kim Clijsters at the 2011 Australian Open, followed by Li Na at the French Open, Petra Kvitova at Wimbledon, Samantha Stosur at the U.S. Open, and current No. 1 Victoria Azarenka at January's Australian Open -- Serena needed only a second or two to formulate a response.
"Hopefully," she said, "it will be six this time -- with me."
She's 17-0 on clay this season and among the favorites heading into the French Open, which she won in 2002.
What would a second title, a decade later, mean to her?
"It would be really intense and really crazy," Serena said. "I mean, obviously there are several people here that want to win. I think I'm one of those people."
Price said a championship at Roland Garros "would be huge" for Serena, because it would make clear that "it doesn't look like she's ready to quit" at 30 years old.
Asked whether her younger daughter is ready to get her name etched on another Grand Slam trophy, Price chuckled.
"For sure," she said. "You know Serena. She's got to be on the list at least once a year, right?"
One challenging step along the way over the next two weeks could come in the quarterfinals, where Serena might have to face three-time major champion Maria Sharapova, who is seeded second and also a popular pick.
"She's such an experienced player that has been under so many different circumstances and achieved so much in her career," Sharapova said. "When she's fit, she's extremely strong on the court and hits a very powerful ball. That makes her very dangerous."
That sounds like a rather fair scouting report for Sharapova, too, even on clay these days. Having once described her movement on the slow red surface as something akin to a "cow on ice," the Russian can get around well on the stuff.
"I'm much more comfortable on this surface. Even though I don't play too many tournaments on it throughout the year, I feel like with every year that has come, and the clay-court season that arrives, I feel physically stronger," Sharapova said. "That's definitely helped me in the recovery process, as well. I'm enjoying it a bit more. Before, I felt like in matches I was saving myself a little bit because I didn't always believe that physically I could play seven matches in difficult, heavy conditions in Europe."
She's coming off her second consecutive title on clay at the Italian Open, where she beat Li in the final Sunday.
Citing a bothersome back, Serena withdrew before she was supposed to face Li in the Rome semifinals. But that feels "a lot better" after treatment, the American said.
If good health is one key to Serena's success, another is the mental boost she gets from having Venus alongside her.
Venus, who turns 32 next month, resumed playing in March after more than six months off the tour. A first-round match Sunday against 19-year-old Paula Ormaechea of Argentina will be her first Grand Slam competition since the first round of the U.S. Open on Aug. 29.
"I just don't know anyone out there who has gone through everything that she's gone through and just remaining completely positive," Serena said about her sister. "It's never easy for anyone who's going through what she's going through. To do what she's doing and play a professional sport is, I think, a whole new level of mental strength. ...
"Everything that she's doing is so inspiring for me."