12:55 PM PT -- We've now spoken to other witnesses at the party who claim Alexander "AE" Edwards was the instigator, as he ran up on stage and initiated physical contact with Travis Scott.

Travis Scott and Tyga's camps are leaving their mark on Cannes, courtesy of an all out melee inside an after-party ... and from the looks of things, a few ice packs will be needed.

TMZ Hip Hop got video showing multiple angles of the altercation, which also involved Cher's boyfriend Alexander "AE" Edwards and 808 Mafia producer Southside -- and it all went down at acclaimed promoter Richie Akiva's event.

Sources familiar with the situation tell us the fight started after both Travis and Tyga were on stage behind the DJ booth ... and when Richie grabbed the mic he gave props to both rappers, saying something to the effect of, “We got T-Raww, AE and Travis in the building.”

We're told Travis seemed pissed he was being lumped in with Tyga -- possibly a Kylie Jenner exes thing -- so, Travis snatched the mic out of Ritchie’s hand, prompting AE to say something to Trav. For context, AE and Tyga are besties.

We're told Travis approached Tyga’s security with threats and stormed offstage ... only to return with Southside moments later.

That's when Southside and AE started going at each other ... at first just pushing, but then AE landed several uppercuts, before Travis pulled AE off Southside, and nearly fell offstage in the process.

Then AE and Travis started tussling across the stage. Of course, once news of the fight started spreading on social media ... many people described it as Travis Scott beating up Tyga.

Despite the madness, no one in either party was seriously hurt and security managed to break things up and Travis and Southside returned to their cars. Richie can also be heard scolding everyone for bringing violence to his party.

Our sources tell us Tyga, AE and the crew stayed until early in the morning as if nothing happened.

AE enjoyed a make-out session with Cher just hours prior on the amfAR Gala red carpet ... boy did he have a story to tell when he got back to the hotel!!!