The 36-year-old is playing her first Grand Slam tournament since giving birth to daughter Alexis Olympia last September and has played only a handful of matches this year.
But the 23-times major champion looked reasonably assured in her opening win against Czech Kristina Pliskova and fellow American Courier thinks she can only get better.
"Look, you would be hard-pressed to find anyone betting against Serena doing the unexpected because she's done it so often in her career," Courier said.
"She needs match play for sure but if she gets through the first three rounds and feels good physically and develops a little bit of confidence then she is probably the favourite, because she is Serena."
Williams is 451st on the WTA rankings and while playing under a protected ranking she was not seeded for the French, which means she is up against Australian 17th seed Ashleigh Barty in a second round blockbuster
"She will not want to leave early because she loves Paris," Courier, winner in 1991 and 1992, said.
"It's hard to say where she is. But she will be ready to fight for it. The draw is tricky but that can play a positive role for Serena because she can't necessarily just work her way into the tournament the way she could if she had an easy draw."
If she beats Barty, 11th seed Julia Goerges could be next, and then there is the possibility of a fourth-round clash with twice former champion Maria Sharapova.
"Barty is a tough Aussie and there are a lot of landmines on her road but none of the others will want to come up against her," Courier said.
