The 25-year-old Frenchman left Walsall on Monday. He joined the Saddlers in August and has figured in 24 games this term but most of his games came as a substitute.
His only goal earned a 1-0 Johnstone’s Paint Trophy win at Rochdale that began Walsall's journey to their first Wembley final.
Manset has faced Cheltenham for Hereford United, scoring in a 1-1 draw at Edgar Street in November 2010 before earning a move to Reading in January 2011. He has since featured for FC Sion, Carlisle United, Coventry City and Antwerp.
His arrival completes a busy 48 hours for Robins boss Paul Buckle, who has also recruited Eliot Richards and Jordan Wynter on 18 month deals, with Wes Burns and Denny Johnstone brought in on loan until the end of the season.
Liverpool youngster Lloyd Jones has also agreed to extend his temporary stay for the duration of the campaign, while Terry Gornell departed and has rejoined Accrington Stanley.