The 19-year-old joins the leaders on loan until the end of the season.
Manager Gary Johnson told the club’s official website that his versatility will be a key factor.
“He’s a midfield player that can play anywhere across the four in midfield, wide or central and can play as a number 10,” he said. “He’s got our work ethic, he’s got our way of playing in his head because that’s the way he plays.
“We’re very pleased to have him because he’s a quality player and he will give very good competition to our small squad. Bournemouth have high hopes for him and this is his first loan.
“To be fair to Bournemouth and Frankie, they’re both happy that he comes in and part of his development is going to be fighting for a place. He’s happy to do that and he seems a very level-headed boy as well.
“He has a really good work-rate. That’s what impressed us.”