The 23-year-old woman, who was eight months pregnant, was found naked, tied up and blindfolded on Wednesday in her apartment in Ustaritz, in the southern Basque region near the Spanish border.
The suspect, who had no fixed address, was detained in nearby Boucau after a high-speed car chase with police. According to reports in France he had a history of mental illness.
The dead woman's partner had found her body and raised the alarm.
An autopsy found that she had suffocated after being gagged. She also had injuries to her face, including a broken nose.
It was not yet known if she had been sexually assaulted.