The 30-year-old has put pen to paper on a one-year deal, with an option of a further 12 months.
Romaric has prior experience of Ligue 1 - he played for Le Mans between 2005 and 2008 before leaving France for Spain, where he joined Sevilla.
A loan spell with Espanyol followed before he moved to Real Zaragoza, and he spent last season at the Aragon outfit, making 14 appearances, before his contract expired.
At Bastia, he will team up again with coach Frédéric Hantz, who he also played under at Le Mans.
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