Liu Shaoyo was shot dead in his apartment on Sunday by police responding to suspected domestic dispute call.
His death has angered members of the Chinese immigrant community who clashed with police on Monday.
China has lodged a complaint calling for its citizens to be protected.
At a press conference on Wednesday, Francois Ormillien, one of the lawyers representing the family, said: "We know that this incident has caused some turmoil.
"The family wished for this press conference to launch an appeal for calm."
Police have said that Mr Liu was shot as he tried to attack an officer with a sharp object.
His family had said earlier that Mr Liu was holding a pair of scissors as he was preparing fish for dinner.
On Wednesday, their lawyers said he had not attacked nor rushed at the officers, and that details of his death remained "extremely obscure".
One of Mr Liu's daughters, who was in the apartment at the time, also gave her account.
"They began to bang on our door and then we heard something we didn't know who it was, by that time I was stricken with panic.
"My father was really trying to hold back the door and then the door opened all of a sudden. A shot was fired. All of this happened in just a few seconds," she was quoted as saying by AFP news agency.
Read more: French Chinese 'at breaking point'
The daughter, who declined to be named, had previously told French media she did not recognise the men at the door as police officers when she looked through the peephole, as they were not in uniform.
The case has sparked anger among Chinese residents in Paris.
Following Monday's violence which left three police officers injured, members of the French Chinese community staged a protest in Paris on Tuesday night.
Beijing has called for French authorities to "guarantee the safety and legal rights and interests of Chinese citizens in France and to treat the reaction of Chinese people to this incident in a rational way".
The family of a Chinese man whose killing has sparked clashes in Paris has called for calm, as they disputed French police's version of events.