The incident was filmed at Richelieu – Drouot Metro station on Tuesday, before the English club's Champions League clash against PSG at the Parc des Princes stadium to the west of Paris.
In the video, which was sent to the Guardian newspaper
, an unidentified black man tries to board the packed train only to be physically pushed away by the Chelsea supporters. Other passengers look on.
The man repeatedly tries to squeeze into the carriage and they aggressively push him back. The film then cuts to the men chanting: "We're racist, we're racist, and that's the way we like it!"
After the video went viral across the web and caused outrage among viewers the French police announced on Wednesday they had opened a probe into "deliberate racial violence on public transport".
The probe will be handled by the specialist STADE team at Paris police which investigate incidents of hooliganism.
"We will work with British police, these people must be known," a French police source told AFP.
London police confirmed that they would assist the French investigation.
"We will examine the footage with a view to seeing if we can apply for football banning orders, preventing people from travelling from future matches," said a New Scotland Yard statement.
For their part Chelsea have condemned the actions of the fans.
"Such behaviour is abhorrent and has no place in football or society. We will support any criminal action against those involved, and should evidence point to involvement of Chelsea season-ticket holders or members the club will take the strongest possible action against them, including banning orders."
The video was filmed by British expat Paul Nolan, who told The Guardian that he was "completely appalled" by what he saw, adding that he felt unsafe filming.
"It was getting quite aggressive and I overhead one of the Chelsea fans say something about stabbing someone. I think he was referring to a Paris Saint-Germain supporter who was on the platform.”
When Chelsea played PSG in last year's competition around one hundred Chelsea fans were involved in running battles with PSG fans in the centre of Paris, in front of shocked locals.
Following the incident on the Paris Metro European football's governing body UEFA condemned the fans' behaviour, but said that because it had occurred outside the stadium, it was not within its jurisdiction to act upon it.
"UEFA condemns all forms of discrimination and we are appalled by the incident which took place in the Paris Metro on Tuesday," the organisation said in a statement.
"However, as it occurred away from the stadium, it is outside UEFA's remit to act. It is a matter for the local authorities to investigate further and UEFA supports any action that is taken."
Sepp Blatter, president of world governing body FIFA, also expressed disgust over what had happened.
"I also condemn the actions of a small group of Chelsea fans in Paris," he wrote on Twitter. "There is no place for racism in football!"
Chelsea fanzine editor David Johnstone expressed fears for the club's reputation in light of the incident.
"I think the majority of Chelsea supporters are disgusted by what's happened," he told BBC radio.
"The 2,000 who were in Paris today (Tuesday) support a Jewish-owned football team where the majority of players are black and foreign."