Arian Foster In Hot Dog Stand Showdown Over N-Word Insult

Arian Foster -- along with his brother and father -- was involved in a heated standoff at a hot dog stand in Houston this weekend ... and it all started with shoe smack talk.

TMZ Sports has footage of Arian, his brother Abdul and father Carl at Yoyo's Hot Dog around 3 AM on Sunday ... and at first, it seems the ex-NFL star is having fun with some local college kids. Foster says the other man's shoes are "awful."

But things quickly took a turn -- witnesses tell us the college students felt Arian took the insults too far, so they began shouting back at him. Someone shouted at Arian, "You're not even relevant anymore, n***a."

Abdul was pissed -- and tried to confront the insult hurler (who we're told is black). Adbul then got physical with 2 people and that's when Arian and Carl rushed in to break the whole thing up.

At one point, Arian says to one of the students, "F**k you, n***a."

Witnesses told us someone threw a hot dog in the melee ... but it was broken up before things escalated into a brawl and everyone left when someone threatened to call police.