"Even as someone who is white this must concern me," Poirier told French sports daily L'Equipe on Tuesday.
"It touches me since I have black team mates, black friends, my wife is of mixed race.
"I can walk the streets freely and I want it to be the case for everyone. It bothers me that it's not the case," the Frenchman added.
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Video footage showed a white Minneapolis police officer kneeling on the neck of Floyd, 46, for nearly nine minutes before he died on May 25, triggering outrage and protests across the United States.
Poirier added that there had been similar issues in France, highlighting the case of 24-year-old black man Adama Traore, who died in 2016 while being driven to a police station following his arrest over an altercation. The circumstances of Traore's death are still under investigation by justice authorities.
Poirier, who signed for the Celtics in 2019, said he wanted to use his standing in the sports world to bring attention to such issues.
"At the time of Adama Traore, I did not have this recognition but now that I have it, I try to use it. The fact that I play for Celtics has an extra impact," he said.
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