Serena Williams is officially OUT of the French Open ... the tennis legend withdrew from the tournament Wednesday, saying she has an Achilles injury that's hurting like hell.
"Struggling to walk," Serena said of the injury. "So that's kind of a tell-tale sign that I should try to recover."
The 39-year-old hurt the lower leg at the U.S. Open in New York earlier this month ... and thought she had given it enough time to heal to be effective in Paris.
But Williams said during her opening-round victory over Kristie Ahn on Monday, she felt the tendon aching -- and decided to pull out of the event.