We model the structure of the lithosphere, its thickness, and seismic anisotropy caused mainly by systematic orientation of olivine crystals, from spatial variations of P wave delay times and the shear wave splitting observed at a dense network of mobile and permanent stations within the French Massif Central (MC). Three major lithosphere domains with different seismic anisotropy are distinguished. A suture in the deep lithosphere limits the thick lithosphere of the Limousin (western MC) characterized by a consistent anisotropic pattern with high velocities dipping to the west. The eastern MC, comprising two different domains with a weakened mantle fabric in the south, shows the high velocities dipping systematically to the east. The suture between the western and eastern MC parallels the major crustal boundary, the late Variscan Sillon Houiller transfer fault in the south and the Tauve-Aigueperse fault in the north, with an offset of 10--20 km to the east. The offset of the crustal and mantle parts of the same suture indicates that the rigid upper crust might be detached from the mantle lithosphere. We suggest that the mantle suture, hidden beneath an allochthonous crust, was reactivated during the Cenozoic extension of the weakened and thinned lithosphere in the south of the eastern MC and predestined a space for the major volcanism (Mont Dore, Cantal). The rigid northern domain, characterized by a thicker lithosphere with a well-preserved mantle fabric, reacted to the extension predominantly by rifting (e.g., Limagne and Roanne Grabens).