Frederic Blancke, 26, said he had returned to the site of the earlier attack on Fiona Jones, 26, because he had left a shoe behind. But when he arrived in his car he saw her sitting by the side of the road, he told the court of assizes in Beauvais, northern France. He took a knife from his car and went to her with the intention of killing her.
'I jumped on her straight away and attacked her on the throat. I don't know how many times I stabbed her. I did it without knowing the consequences of my act. I was in panic. I know I killed her but I didn't think about the consequences - it was just that moment then,' he said.
Mrs Jones, from Kingsbury, Warwickshire, who was on holiday in France with her husband Mark to celebrate their first wedding anniversary, had gone out on a bicycle ride. Her body was found six months after she disappeared in August 1989.
Mr Jones, 30, his wife's parents Bruce and Pat Cottrill, and their two sons Jonathan and Simon who come from Colwyn Bay, Clwyd, Wales, were in court yesterday to hear Mr Blancke describe the killing.
Asked why he had decided to carry out the killing, Mr Blancke replied: 'I don't know why I panicked like that. Perhaps to hide my earlier error, perhaps to make her disappear - I don't know. I try to understand, I will never understand.'
Mr Blancke, a hospital radiographer, said he had been angry with his girlfriend because she had left his flat without saying and left the key. Then on the Saturday before the attack he had telephoned her to try to meet up with her that evening. She said she was feeling unwell and could not go out.
That same evening he saw her hand-in-hand with another man. He made a frantic search for her in the town but was unable to find her.
Then on the Monday of the killing he decided again to go to look for her. As part of the search he drove to her parents' house at Lassigny. It was when he was returning from there that he saw Mrs Jones riding her bicycle through the wooded countryside and attacked her. Mr Blancke said he wanted to explain to her family what had happened but could not.
He later returned again to pick up the bicycle which he had thrown in a field and took it to a canal where he dumped it. Asked why he had done what he did, Mr Blancke replied: 'I was ashamed, I was cowardly.'
The hearing was adjourned until today when lawyers representing the prosecution, defence and Mrs Jones's family will make their closing speeches. The jury will then retire with the three judges to consider their verdict and the sentence.