The tale goes like this:
Tristan's mother was sister to Marc, who was king.
She was called Blanchefleur.
Rivalin had come to assist her brother in battle - it varies on why (he was vassal, etc.)
He was gravely injured in battle. He lay to die.
And Blanchefleur somehow this man had struck her, and she fell low until she said to her nurse, 'This dead man Rivalin is killing me'. And so it was contrived she should go to see him.
So she came to be pregnant with Tristan.
Rivalin was to sail back to his homeland after his recovery, and Blanchefleur came to him in grave fear of her brother, now she was pregnant.
So Rivalin married her and took her back.
Away he went to battle.
She waited for him, pregnant.
But instead she saw a ship with black sails coming in from the battle.
And she went into labour, knowing her husband was dead, and her last was to give him his name, Tristan, and so he went to his foster father, who brought him up.