TMZ Sports has obtained police docs from June 20, 1997 ... when Marrone -- a Georgia Tech assistant at the time -- was popped for doing 57 MPH in a 35 in Daytona Beach Shores, Florida.

According to the docs ... Marrone was pulled over at 11:59 AM in a 1997 Buick with fellow GT assistant coach Lance Thompson riding shotgun.

Cops say when they checked Doug's record ... they found he had a suspended license stemming from a previously unpaid ticket -- and they slapped the cuffs on him.

Turns out ... Marrone needed his boss -- legendary college football coach George O'Leary -- to get him out of jail ... 'cause cops say O'Leary paid Marrone's $100 bond!!!

Of course, Marrone's star running back suffered a similar fate last Thursday when Fournette was pulled over at a car wash and arrested for driving on a suspended license.

Marrone announced to reporters Tuesday Fournette wouldn't be punished for the incident ... saying he knows firsthand it ain't exactly the biggest deal.

By the way, Doug also wasn't kiddin' when he said it hurt being put in cuffs back then ... 'cause cops say he tipped the scales at 6'5", 305 pounds!!

Oh, and cops also say he had a tattoo of a rose on his upper back.