The Romanian third seed, beaten by Maria Sharapova in the 2014 final, has been in great form during the claycourt season, winning the Madrid title and reaching the Rome final where she rolled her ankle against Elina Svitolina.
"Today is much better. Actually, today was the first time when I was running on court, when I played some points," Halep told reporters. "It's getting better. Tomorrow I have another ultrasound to see if the ligament is still broken or it's fixed.
"Looks better. So I hope is gonna be okay."
With Serena Williams and Maria Sharapova, who between them have won four of the last five French Opens, both absent and defending champion Garbine Muguruza struggling for form, a fit Halep would have a great chance to claim a first major.
However, she said just making sure she can face Slovakia's Jana Cepelova in the first round is her only immediate goal as she recovers from the ligament tear in her right ankle.
"I will do everything I can to start this tournament as good as I can, to be able to play this tournament first, and then we will see what is gonna happen," she said.
"I'm just trying to get better soon, to get stronger, because I need that, to be able to move."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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