The circumstances of the attack were unclear.
Some witnesses said the suspect made remarks "linked to Islam" but the police urged caution, saying the killer's motives were unknown.
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A resident of the high-rise building in the city's 11th district said he heard a man "crying for help" at around 1000 GMT.
"I looked out the window and saw a man lying on the ground. There was a lot of blood.
"There was another man standing beside him, dressed in a white djellaba (loose-fitting tunic worn by some Muslims). He fell to his knees and prayed until the police came to take him away," 21-year-old Thomas told AFP.
Another resident, 64-year-old Francois Petitjean, described a harrowing scene.
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"When I arrived in the hall of the building I saw a body lying in a pool of blood, in front of the postboxes. It was carnage. I went out and then saw another person covered in blood," he said, expressing shock.
Police had sealed off a section of the street around the building. No further details on the suspect or the victims were immediately available.
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