Narumi Kurosaki, 21, was studying French at the university of Besancon in the country's east before she went missing on the night of December 4.
Her body has yet to be found but her Chilean ex-boyfriend, who is believed to have fled to his home country, is suspected of her murder.
“The investigation has shown he was in France, in Besancon, at the time of her disappearance,” prosecutor Edwige Roux-Morizot told a press conference.
The prosecutor ruled out suicide, describing Kurosaki as a “young girl full of life” who was happy in a new relationship.
“There is sufficient evidence to launch a murder investigation,” she told a press conference.
“Several students living on the same floor (of her student residence) heard a loud cry on the night of December 4-5. From that moment on, there was no trace of Narumi.”
Anne-Laure Saillet, a 20-year-old student, told AFP she heard “bangs on the doors and furniture and afterwards I heard a very shrill cry, very sharp and loud. It was a woman's cry.
“At first I thought it was a horror film but when it continued I became worried.”
Roux-Morizot said tests were being carried out on reddish traces found on the steps of the building to determine whether they were bloodstains.
She described the Chilean teaching assistant, whom Kurosaki met in Japan but from whom she later split, as having an “intrusive, disturbing personality”.