Brisbane man Benjamin Milward, 25, was identified as the only person of interest in the murder investigation during a press conference held by Queensland Police on Friday.
Police said Milward was known to frequent the South Bank area, but advised people not to approach him.
The body of 21-year-old French women Sophie Collumbet was found in a park in Brisbane on Friday morning.
Police say the Griffith University business student had been bashed in the head.
Queensland Police Detective Inspector Rod Kemp says he hopes CCTV will help investigators piece together what happened.
“Some of the vision is grainy. There’s possible footage at 2 and 3am. And there’s clearly earlier vision on Thursday morning of her.”
Authorities have moved to reassure people Brisbane is a safe city for young foreigners following the murder of a fourth international student in little over four months.
LISTEN: Authorities reassure people after murder
The deaths are not connected, and, in all but the latest case, police have made arrests.
In November, South Korean Eunji Ban was found bashed in a park.
Just days before Christmas, South Korean Min Tae Kim was found buried in a backyard.
Last month, Singaporean Meena Narayananwas found stabbed in a hotel room.
Queensland Police Commissioner Ian Stewart has told the ABC violent crime can happen anywhere.
“One of the challenges we have in our large metropolitan cities right throughout this country is that we try our hardest to keep everyone safe but there are always those tragedies.”
In the latest case, police have no suspects.
But Queensland’s Premier Campbell Newman maintains Brisbane is a safe place.
“I believe it’s safe not only for students, but it’s safe for Brisbane residents. I’m obviously very saddened and troubled by this latest case, and I hope the police can catch someone as soon as possible.”
The Queensland Tourism Industry Council says visitors to Brisbane have nothing to fear.
Chief executive Daniel Gschwind says there is a difference between the random acts of violence in Brisbane and the violence Indian students experienced in Melbourne a few years ago.
“I don’t think there’s (any) indication that this is some systemic situation here. These are genuinely random acts of violence that unfortunately do occur in just about any community. And we have to make sure — we have an obligation as hosts to our visitors to make sure — that everybody’s informed about the risks and dangers that may exist, whether that’s natural dangers, animals, the sea, the surf, the traffic, or in situations like this.”