The formation of a core region with improved electron confinement is reported in the recent full current drive operation of Tore Supra, where the plasma current is sustained with the lower hybrid (LH) wave. Current profile evolution and thermal electron transport coefficients are assessed directly by using the data of the new fast electron bremsstrahlung tomography that provides the most accurate determination of the LH current and power deposition profiles. The spontaneous rise of the core electron temperature observed a few seconds after the application of the LH power is ascribed to a bifurcation towards a state of reduced electron transport. The role of the magnetic shear is invoked to partly stabilize the anomalous electron turbulence. The electron temperature transition occurs when the q-profile evolves towards a non-inductive state with a non-monotonic shape, i.e. when the magnetic shear in the plasma core is reduced to close to zero. The improved core confinement phase is often terminated by a sudden MHD activity when the minimum q approaches 2.