9:42 AM PT -- Jaguars head coach Doug Marrone says he's spoken with Fournette, who claims the heckler had been shouting "racial slurs" at him and that's why he reacted the way he did.
When asked if there were any witnesses to back up Fournette's claim, Marrone said, "I trust the player."
9:39 AM PT -- Matt Stafford's wife, Kelly, has just weighed in ... PRAISING Fournette for "the way he stood up for himself."
Kelly noted, "'Fans' probably said way worse things to him ... but yet he will lose money because he responded."
The message -- Kelly is sick of players like Fournette getting heckled by people in the stands.
Jacksonville Jaguars running back Leonard Fournette was so rattled during the loss to the Tennessee Titans on Thursday, he got into it with a fan ... and threatened to beat the guy's ass.
TMZ Sports has footage of Fournette on the sidelines in the 4th quarter of the Jags' 30-9 loss at Nissan Stadium in Nashville ... where the RB angrily tells the fan, "Listen, you're too old for that. I will beat your ass!"
Two men who appear to be Jaguars staffers grab Leonard and try to walk him away -- but minutes later, Fournette begins to jaw at the fan again ... repeating his threat.
"Facts, you're too old for that," Fournette says while sitting on the team bench ... "You're too old for that. Chill out. I'm not worried about you. You want to come down here?? I'll whoop your ass."
The Jags lost the game and Fournette was only held to 36 rushing yards on 14 carries.
Fournette has been irritable lately -- just a few weeks ago, he was ejected from the Buffalo Bills game for fighting Shaq Lawson ... and then tried to continue the scrap in the stadium tunnel.
Fournette was hit with a 1-game suspension for the Buffalo incident -- and later apologized to "the fans and kids out there."
"Was totally out of character was in the heat of the moment in a important game," Fournette posted on social media ... "emotions got the best of me apologize again to you all."
Fournette has never been afraid of a fight -- back in college, he got into it with LSU offensive lineman Garrett Brumfield outside of Tiger Stadium in Baton Rouge.
LSU officials insisted the guys were just messin' around.
But, one thing's for sure ... if Fournette threatens to beat your ass, he's willing to back it up.