The French atomic time scale TA(F), which is computed with data from 20 to 30 industrial caesium standards, depending on the given period of time, located in nine institutions or companies located on French soil, is aiming at providing a common stable national frequency reference to the contributing institutions. To improve its stability, it was decided in 2002 to steer it to the LNE-SYRTE Primary Frequency Standards (PFS). The frequency of TA(F) was first slowly corrected monthly to compensate the drift without disturbing the 30 d relative frequency stability of the time scale. Once close enough to the SI second, the time scale was steered monthly to the frequency data issued from the LNESYRTE PFS, providing that way a more stable reference, improved by a factor 2 with respect to the former system. We describe the steering applied to TA(F) and show the results in terms of relative stability with respect to TAI, or by comparing TA(F) to the SI second on the geoid as published monthly by the BIPM in its Circular T. We apply this steering since July 2006. With this method, the departure over 30 d intervals of TA(F) from the SI second on the Geoid is globally maintained inside the limits 1.8 × 10-15. Within these limits, the TA(F) scale unit interval is in agreement with the SI second, a result which was made possible thanks to the four PFS currently in operation in the LNE-SYRTE.