The move was arranged before today's managerial departure, and the 21-year-old will join up with the Tudors ahead of their game against Wingate & Finchley in the FA Trophy on Saturday.
Tudors are managed by former Town youth coach Joe Deeney, who has overseen a bit of a reunion of former and current Hatters players, with his side including the likes of Jack Snelus, Kavan Cotter and current Town youth team striker Connor Tomlinson.
Frankie has already enjoyed a loan spell at Oxford City this season, where he played in the first round of the Emirates FA Cup, as they were knocked out by Tranmere Rovers in a replay, making seven appearances in total.
Good luck for the rest of the campaign, Frankie!