12:19 PM PT -- TMZ Sports has obtained a photo of the "exploded eyeball" injury ... and warning, it's pretty gnarly.
The person who shot the photo tells us everyone in the area was "freaking out" -- but fortunately, medical personnel were able to keep their composure and treat the victim.
Brooks Koepka also issued a statement saying, "I was deeply hurt and saddened by the tragic accident that occurred when a shot I hit off the 6th tee struck Miss Remande."
"I spoke to her at the time on the golf course and after now learning her condition is worse than first thought, I have made contact with her/family to offer my sincere and heartfelt sympathy."
"I am heartbroken by the incident. My thoughts remain with Miss Remande and her family, and I have asked to be kept informed on her condition."
The woman lying on the ground in this photo claims her eyeball "exploded" when she was struck by a Brooks Koepka tee shot at the Ryder Cup ... and now she's threatening to sue.
49-year-old Corine Remande was watching the USA vs. Europe event on Friday morning at the Le Golf National club in Saint-Quentin-en-Yvelines (near Paris) ... when Koepka's 6th hole tee shot hooked left and smacked her in the face.
Remande crumpled to the ground while fans and medical personnel rushed to tend to her. Koepka also raced over to check on her and gave her a signed glove.
The woman was transported to a local eye specialist. It was revealed she had suffered a "fracture of the right socket and the explosion of the eyeball."
Now, Remande is pointing the finger at Ryder Cup tournament officials -- claiming they failed to properly warn and protect spectators from wild golf shots.
She's considering her legal options -- but hasn't filed a lawsuit yet.
However, a Ryder Cup spokesperson says "fore" was shouted several times before it hit the fan.
Koepka commented on the incident after winning his match with Tony Finau, saying "It doesn't feel good, it really doesn't. You feel terrible for them."
"You don't want to hit anybody in the face, especially not a woman, and it's not a good feeling."