This paper proposes a fixture-free 2D sewing system using a dual-arm manipulator, i.e., the seam lines of the top and bottom fabric parts are the same. The proposed 2D sewing system sews two stacked fabric parts together along a desired seam line printed on the top fabric part without the use of a fixture. In the proposed system, the set of aligned and stacked fabric parts is held by the end-effectors of the dual-arm manipulator in coordination. The dual-arm manipulator controls the motion of the fabric parts on the flat sewing table stitch by stitch in coordination, while keeping the manipulated fabric parts flat using the internal force applied to the set of fabric parts. A novel vision-based seam line tracking control is proposed to control the motion of the set of fabric parts along the printed seam line on the top fabric part. The convergence of the tracking error is analyzed for sewing along both straight and curved seam lines and is shown to be specified by the control parameters. Sewing experiments show that the tracking error converges to zero as analyzed. The sewing experiments also show that the newly proposed trajectory generation method, which synchronizes the coordinated motion of the manipulators and the motion of the sewing needle, is essential for achieving accurate sewing.