The two officers were driving home drunk at around 4am on Thursday when their unmarked police car collided with the delivery van, according to reports in the French media.
The victim, aged 40, who was delivering bread around Paris, died shortly after from the injuries sustained in the collision.
The officers had reportedly been out in a nightclub near the Champs-Elysées and were driving north in their unmarked car.
CCTV footage is said to show the pair driving at high speeds and blazing through red lights.
On Boulevard Sebastopol, a one-way thoroughfare that leads to Gare de l'Est railway station, the officers crashed into the delivery van. It had initially been reported that the victim was on foot at the time of the accident.
The police were taken into custody where they allegedly refused to do a breath test.
Rush hour traffic was affected on Thursday morning as dozens of police officers cordoned off the intersection where the collision occurred.
If it's proven the police were drunk at the wheel, the death of the delivery driver will count as another black name against the capital's police force.
Paris police have earned themselves somewhat of a bad reputation in recent months – mainly thanks to the city's criminal investigation unit, known as the Police judiciare.
The unit, seen as France's answer to the FBI, has been embroiled in scandal after scandal – including 'losing' 52 kilos of confiscated cocaine (worth a cool €2.5 million), the alleged rape of a Canadian tourist at the police headquarters, and the force's chief being suspended over allegations he leaked details of a probe to a fellow top officer under investigation.