The French atomic time scale TA(F), which is computed with data from about 20 industrial caesium standards located in nine French institutions, aims to provide a stable national frequency reference to the contributing institutions. To improve its stability, it was decided a few years ago to steer the time scale, which up to that date was free running, on the LNE-SYRTE primary frequency standards (PFS). The frequency of TA(F) was first slowly corrected monthly by an arbitrary given frequency offset with respect to TAI, 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 LNE-SYRTE PFS, in that way providing a more stable reference. 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) with the SI second on the geoid as published monthly by the BIPM in its Circular T. When applying this steering during recent years, the departure over 30 d intervals of TA(F) from the SI second on the geoid was maintained inside the limits ±3 × 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.