Mets Legend John Franco -- HUGE MO'NE DAVIS FAN ... I Hope She Makes the Majors!

She's only 13, but Mo'ne Davis could be the 1st woman to break down the MLB gender barrier --so says Mets legend John Franco who says he's a HUGE fan of the female fireballer.

Franco -- who pitched in the Majors for 21 years -- was out in NYC on Monday and told us he's super impressed with Davis ... who's broken out as the star pitcher in the Little League World Series.

"She's good. She's really good. She's great for baseball."

FYI -- Davis is DOMINATING at the LLWS ... and just last week, she threw a complete game shutout against South Nashville ... striking out 8 (with no walks).

In fact, Franco says he probably couldn't get a hit off Davis if they ever faced off.

Then again, Franco only recorded 3 hits in his entire MLB career ... but you get the point.