During their late pulsating phase, AGB stars expel most of their mass in the form of massive dusty envelopes, an event that largely controls the composition of interstellar matter. The envelopes, however, are distant and opaque to visible and NIR radiation: Their structure remains poorly known and the mass-loss process poorly understood. Millimeter-wave interferometry is the optimal investigative tool for this purpose. The circumstellar envelope IRC +10 216 and its central star, the C-rich TP-AGB star closest to the Sun, are the best objects for such an investigation. Two years ago, we reported on IRAM 30-m telescope CO(2-1) line emission observations in that envelope (HPBW 11). We now report much higher angular resolution observations of CO(2-1), CO(1-0), CN(2-1) and C$_4$H(24-23) made with the SMA, PdB and ALMA interferometers (with synthesized half-power beamwidths of 3, 1 and 0.3, respectively). Although the envelope appears more intricate at high resolution, its prevailing structure remains a pattern of thin, nearly concentric shells. Outside the small (r<0.3) dust formation zone, the gas appears to expand radially at a constant velocity, 14.5 km/s, with small turbulent motions. Based on that property, we have reconstructed the 3-D structure of the outer envelope and have derived the gas temperature and density radial profiles in the inner (r<25) envelope. The over-dense shells have spherical or slightly oblate shapes and typically extend over a few steradians, implying isotropic mass loss. The regular spacing of shells in the outer envelope supports the model of a binary star system with a period of 700 years and a near face-on elliptical orbit. The companion fly-by triggers enhanced episodes of mass loss near periastron. The densification of the shell pattern observed in the central part of the envelope suggests a more complex scenario for the last few thousand years.