The victim’s body, handcuffed and partly burned, was found on Saturday in a wood in Chantilly, north of the capital, and was later identified as 19-year-old Susanna by her parents.
She been badly beaten and was killed by a knife blow to the neck, according to a post-mortem examination.
There was no trace of sexual assault but officials believe the killer may have set fire to the body to destroy evidence.
The blonde young woman went missing on Friday night after heading home in a taxi, following a night out at the Scala nightclub in central Paris, whose owners have been questioned by police.
According to investigators, she sent a text message to a friend saying the taxi driver “did not look right.”
Investigators are looking into a possible connection with an attack in February in which another Swedish woman was raped on her taxi ride home, then pushed out of the car in a wood west of Paris.
According to newspaper Aftonbladet, the victim was studying French at the Sorbonne, working part-time in a cafe and living in a shared flat in Paris.