Cumbrians boss Keith Curle signed the French midfielder who left Rochdale by mutual consent at the end of last season.
The 23-year-old made 42 appearances for Dale after joining from Sheffield Wednesday in 2013, and featured twice for France Under-18s in 2009.
Speaking to the official club website, Curle said : “He is an exciting player. I think people will have seen the signings up to now as players who will come in and do an important job for us, without getting bums off seats because of something they’ve done. Bastien is a player who will get people on their feet a lot.
“There are goals in the team already, but I know we still need a few more. We can add to what we have by creating a supply line, and Bastien will do that for us.
“He’ll have work to do in attack and defence but, going forward, he can move the ball and he is what I would describe as a dynamic player.
“He gets about the pitch with or without the ball and he can link play up just by seeing a pass quickly. He’s a very intelligent player and I think we will all enjoy watching him.”