The officers were all found guilty of the manslaughter of Amadou Koumé.
Three French police officers have been convicted over the death of a black man during his arrest in Paris in 2015.
The officers were all found guilty of manslaughter on Tuesday and handed 15-month suspended prison sentences.
Two of the defendants had strangled Amadou Koumé and pressed their knees on him during the arrest. The third man on trial had been the senior officer on duty.
Koumé's family have welcomed the guilty verdicts from the Paris criminal court but says the suspended sentences are "lenient".
The 33-year-old father, who suffered from dementia, died in March 2015 after he was pinned to the ground by officers in a bar, put in a chokehold and left handcuffed on his front for more than six minutes.
An autopsy later revealed that the cause of death was "slow mechanical asphyxiation" inside the police van.
The three officers were all found guilty of "faults" that led to Koumé's death, including an "insufficiently controlled" use of force and leaving the 33-year-old in a vulnerable position without inquiring about his health. The verdict can be appealed.
"It is a satisfaction to hear the word guilty in such a case, but the sentence is relatively lenient, so there is a piece of justice that has been done," said Eddy Arneton, the Koumé family lawyer.
"It will not bring back Amadou, but his family now knows precisely the circumstances in which he died and also knows that his death was caused by police officers, so it is a step, and we welcome it as such," he added.
Koumé's death came five years before the killing of George Floyd in the United States, which prompted global protests against racial discrimination.
In 2020, the French government pledged "zero tolerance" for racism within the police, and subsequently stopped teaching officers the controversial "chokehold" arrest technique.
France's government has also been criticised for a controversial new "global security law" that would punish citizens who maliciously share images that identify operating police officers.
Human rights groups and journalists feared the bill would curtail press freedoms and lead to less police accountability.
The law was backed by MPs but was rejected by the country's Constitutional Council last year.