Terror Train Hero Alek Skarlatos -- Fight Is On to Score First Interview

Alek Skarlatos -- one of the heroes who took down the terrorist on a French train -- unwittingly started a media war ... and his parents are taking calls from huge names in news and entertainment.

Alek's dad, Emanuel Skarlatos, tells us his phone has been ringing off the hook since news of Alek's bravery got out. He says producers from ABC, FOX News, MSNBC ... and Jimmy Kimmel have called trying to secure the first sit-down with the 22-year-old National Guard member.

And get this ... being first could be crucial. Alek's mom, Karen, says her son would like to do just ONE interview, instead of making the usual rounds -- though he understands that might be tough, considering how huge the story is now.

Mom and dad say they're heading to NYC soon to greet Alek when he lands.