TMZ released the footage on Monday, following the 30-9 setback on Thursday at Nissan Stadium in Nashville.
"Listen, you're too old for that. I will beat your [expletive]," Fournette tells the fan.
The second-year running back went up to the edge of the stands to talk with the fan, before being escorted back to the bench by team staff members. Fournette also walked down to some Jaguars fans to shake hands. He continued the back-and-forth later in the video, while sitting on the Jaguars' bench.
"Just want to apologize to the fans and kids out there was totally out of character was in the heat of the moment in an important game, emotions got the best of me apologize again to you all," Fournette tweeted following that incident.
Marrone said that he saw the video of Fournette prior to the Jaguars' Monday walkthrough. He met with Fournette on the field to discuss the incident.
"He said there was a racial slur. That's what was told to me," Marrone said.
The coach said Fournette was not aware of the video.
"I trust the player ... stadium security is involved, hopefully. No one wants that stuff around this game," Marrone said.
Fournette, 23, was the No. 4 overall pick in the 2017 NFL Draft. He has 350 yards and four touchdowns on 104 carries in six games this season for Jacksonville.