Da Silva has denied her murder but admits he took O'Keefe home, where they got into an argument.
He said he handed her a sleeping bag and sent her on her way.
Ms O'Keefe's mother Susan told the New Zealand Herald in 2001 that her daughter had planned to leave France on January 2.
She wanted to spend a few days in New York before returning to Wellington to look for another contract.
But Ms O'Keefe had to leave her hostel on New Year's Eve and was worried about where she would stay for her last two nights in France.
A lawyer acting for the family, Caty Richard, said Ms O'Keefe handed back her keys to the hostel that day and planned to meet a French friend, who was an hour late.
"She called an Australian friend, but he was also an hour late, so she set off on a suburban train to head to her French friend's house, and met this young man, who must have sensed her vulnerability."
Her body was found at the Quartier des Musiciens housing estate - an area west of Paris notorious for teenage gang activity.
Speaking at the opening of the four-day trial, Ms O'Keefe's sister Denise said she wanted answers.
"I hope he'll be put away for a long time."
A verdict is expected on Friday.
Ms O'Keefe's mother said in 2001 that her daughter had liked New Zealand because it was easy to find work and she enjoyed tramping and mountain climbing.
She had worked at Air New Zealand in Auckland, and Work and Income and Housing New Zealand in Wellington.