If you have found a valid combination of lattice + basis, you should be able to construct the crystal structure using the lattice in combination with the basis. So do check that. Note that there are many different sets of basis vectors that allow you to do that, and there is no hard rule for choosing one set of basis vectors over the other. However, it is conventional to choose atoms that are closest to a lattice point and that reside at least partly within the unit cell. Therefore, to construct the fcc structure using a conventional unit cell, you typically put the atoms at 0,0 and those at (0.5,0.5,0), (0.5,0,0.5), (0,0.5,0.5) in the basis.