Makoma, 18, has represented France at under-16 level and was most recently playing for RC Lens under-19 academy.
The versatile midfielder has played for the Bluebirds in several of our pre-season friendlies, including the 2-1 win against Lancaster City t the Giant Axe on Tuesday night.
He will play his first game as a Barrow player tomorrow when they travel to National League North side Stockport County.