The suspect, a 69-year-old French man, has confessed to a "pathological" hatred for foreigners and spent nearly a day in a psychiatric facility before he was returned to police custody on Sunday, authorities said.
The shooting at a Kurdish cultural centre and a nearby hairdressing salon on Friday sparked panic in the city's bustling 10th district, home to numerous shops and restaurants and a large Kurdish population.
Three others were wounded in the attack but none were in a life-threatening condition, with one out of hospital.
The violence has revived the trauma of three unresolved murders of Kurds in 2013 that many blame on Turkey.
Many in the Kurdish community have expressed anger at the French security services, saying they had done too little to prevent the shooting.
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