The thickness of freshly made soap films is usually in the micron range, and interference colors make thickness fluctuations easily visible. Circular patterns of constant thickness are commonly observed, either a thin film disc in a thicker film or the reverse. In this Letter, we evidence the line tension at the origin of these circular patterns. Using a well controlled soap film preparation, we produce a piece of thin film surrounded by a thicker film. The thickness profile, measured with a spectral camera, leads to a line tension of the order of 0.1 nN which drives the relaxation of the thin film shape, initially very elongated, toward a circular shape.A balance between line tension and air friction leads to a quantitative prediction of the relaxation process. Such a line tension is expected to play a role in the production of marginal regeneration patches, involved in soap film drainage and stability.