Demonstrators had gathered outside a police station on Monday to pay homage to the slain man.
His family denies police reports that he attacked an officer with scissors as they responded to reports of a domestic dispute at his home.
China has formally complained, calling on France to protect its nationals.
The 56-year-old man - father of-five Liu Shaoyo - was shot dead on Sunday night in Paris's 19th arrondissement (district).
Police say he attacked an officer with a sharp object as soon as he came to the door and the officer was only saved by his bullet-proof vest. Another officer then shot him dead.
But the family lawyer says it "totally disputes" this account.
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One of the man's daughters told French media that her father, who spoke little French, had gone to the door holding a pair of scissors he had been using to prepare fish.
"They smashed the door in, the shot went off and my father ended up on the floor," she told the Parisian newspaper.
China's foreign affairs ministry has lodged an official protest, urging French authorities to do all they can to shed light on the incident and to protect its nationals' "security and rights".
China's intervention is unusual, says the BBC's Hugh Schofield in Paris. The government in Beijing has spoken out in the past about the threat to Chinese tourists in Paris from criminal gangs, but this is the first time it has implicitly criticised an action by French police.
The police watchdog is due to interview the family later on Tuesday.
At least 150 people took part in Monday's protest, some shouting "Murderers!"
There were accusations of police brutality last month, after a young black man said police had sodomised him with a truncheon.