The Syrian man, who denies the offence, was picked up Thursday in the southwestern town of Mont-de-Marsan, four days after the woman's body was discovered.
The 23-year-old man, who is known to police for violent behaviour, was charged after his DNA, already held on a national register, was discovered on the victim, prosecutor Olivier Janson said. Investigators found her mobile telephone and her sim card during a search of his home.
Three other men — an Algerian, a Moroccan and a Tunisian — were freed after initially being detained in connection with the case. They will be deported, however, as they were in France illegally, the prosecutor said.
A passer-by discovered the body of Johanna Blanes beneath a railway line in her home town of Saint-Pierre-du-Mont, around 100 kilometres (60 miles) south of Bordeaux and a short drive from Mont-de-Marsan. Janson said a post-mortem had determined she was strangled after being raped.
The other three men were briefly held before investigators concluded there was no evidence more than one person was responsible for the assault. They are now in detention with a view to their deportation, Janson said.