In March 2001, the commissioning instrument of the VLTI, VINCI, succeeded in obtaining its first fringes by linking two 40cm aperture siderostats on a 16m baseline. During the first year of operation, thousands of interferometric observations on different baselines were carried out, with the technical goal of characterizing this complex system. We report in this paper these first measurements and estimate the main parameters of the atmospheric and internal turbulence along the complete light path. We first illustrate the degradation of the visibility accuracy caused by the differential piston and evaluate the contribution of the internal optical path fluctuations with respect to the atmospheric ones. The stability of the VLTI complex is demonstrated, which enabled us to record easily fringes with Unit Telescopes (UTs) on baselines as long as 102.5 m (November 2001). In the last part, infrared measurements of the atmospheric differential piston are reported. They were obtained with the siderostats on two different baselines ranging from 16m to 66m. Estimations of the coherence time at Cerro Paranal are derived from these commissioning data and compared to the values predicted by the Astronomic Site Monitor (ASM). Finally, constraints on the outer scale length are discussed.