The Gypsy King was seen with Robert Kelbie (38) when he aimed a kick at the car after the driver refused to let him in after a boozy afternoon.
In the short video, Fury is seen being held up by father John as he stumbles towards the white taxi in the middle of the day.
The 33-year-old then leans against the Renault to help him in his attempts to open a locked rear door on the driver's side.
However, the driver hand gestures out of the window, apparently indicating he is not interested in picking up the fare.
The car then drives away with Fury aiming one last frustrated kick at the vehicle.
Among those in the retired heavyweight’s entourage is Kelbie, of Ratho, Edinburgh, who is seen leaning through the passenger’s side window while Fury tries to open the door before it takes off without them.
Kelbie, who previously admitted mortgage fraud in 2012, is well-known to Scottish police and has survived three assassination attempts.
In an Instagram story post, Fury is later shown on a four-mile run through the city with father John on Thursday morning, when he says: "Nice run dad this morning through the city."
John then comments: "Back at it. Too many we had last night." Tyson then asks his father: "Strong beer wasn't it dad?"
John then replies: "Strongest I have had in a while."
Convicted fraudster, Kelbie, who has links to the Lyons crime clan, uploaded pictures to his Instagram in the resort town that included footage of the boxer and his dad with pints of Stella at a roadside bar.
The clip appears to have been taken shortly before the taxi incident.
Kelbie became pals with Tyson after allegedly landing a job working with him two years ago.
He claimed to have served as director of talent for MTK Global, the boxing promotions firm linked to mobster Kinahan, which advised Fury, former middleweight and super-middleweight champion Billie Joe Saunders (32), and Scottish light-welterweight world title holder Josh Taylor (31).
Fury, Saunders and Taylor have no links to crime.
MTK Global was put out of business ahead of the Gypsy King’s Wembley triumph last month when US cops put a $5 million bounty on founder Kinahan.
Fury, who retired after beating Dillian Whyte last month, has been in France for the last several days enjoying his newfound time off and has been spotted on a yacht as well as at different restaurants and watering holes in the country.
He has also posted multiple clips of him and his wife Paris on his Instagram stories, including one where he is seen asking her to hand him a beer next to him while he relaxed on a sun lounger.
Paris obliged with a smile on her face, and a pleased Fury captioned the video: "If Carlsberg did wives."
Tyson Fury also described sanctions against Daniel Kinahan as "nowt to do with me" when he said he has "absolutely zero" business with the crime boss.