Gore, who finished at 14-under-par 275, moved up from the Nationwide Tour last month. He led by four strokes at 16-under after he birdied No. 13, but couldn't hold that pace.
Franco had a 24-foot birdie putt that would have tied Gore, but came up just short at the 18th to finish with a 3-under 69 in his final round.
"It was pretty incredible," said Gore, who shot a 59 during one of his three Nationwide Tour wins this year. "I'm lucky I can even talk."
Ben Crane shot a 67 in his final round to take third place at 11-under 277. Tim Herron (70) finished one stroke further back in fourth.