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We report on the dependence of the frequency-to-intensity noise conversion in the locking of an ultrafast laser against a high-finesse optical enhancement resonator from the carrier envelope offset frequency. By a proper combination of the cavity finesse and laser carrier envelope offset frequency, it is possible to optimize the signal-to-noise ratio of the laser intensity trapped into the optical resonator. In this paper, we describe the effect of the laser-enhancement cavity coupling on the intracavity power relative noise, and we demonstrate both theoretically and experimentally its reduction.