The far-infrared fine-structure line [C II] at 1900.5 GHz is known to be one of the brightest cooling lines in local galaxies, and therefore it has been suggested to be an efficient tracer for star formation in very high redshift galaxies. However, recent results for galaxies at z > 6 have yielded numerous non-detections in star-forming galaxies, except for quasars and submillimetre galaxies. We report the results of ALMA observations of two lensed, star-forming galaxies at z = 6.029 and z = 6.703. The galaxy A383-5.1 (star formation rate [SFR] of 3.2 M-circle dot yr(-1) and magnification of mu = 11.4 +/- 1.9) shows a line detection with L-[C II] = 8.9 x 10(6) L-circle dot, making it the lowest L-[C II] detection at z > 6. For MS0451-H (SFR = 0.4 M-circle dot yr(-1) and mu = 100 +/- 20) we provide an upper limit of L-[C II] < 3 x 10(5) L-circle dot, which is 1 dex below the local SFR-L-[C II] relations. The results are consistent with predictions for low-metallicity galaxies at z > 6; however, other effects could also play a role in terms of decreasing L-[CII]. The detection of A383-5.1 is encouraging and suggests that detections are possible, but much fainter than initially predicted.