This paper focuses on the Femtocell spectrum access problems when a certain amount of Femto Base Stations (FBS) are underlying in a two-tier cellular network, where the Macro Base Stations (MBS) are adopting Fractional Frequency Reuse (FFR) strategy. Under the first-tier outage constraints, the FBS transmission capacity in an analytic form has been presented. It is found via the relevant bound analysis that the optimal Femtocell spectrum access rate depends only on the basic configuration parameters of the Macrocell FFR, regardless the aspects of Femto transmit power and required QoS criteria. Consequently, the optimal Femtocell spectrum access algorithm is proposed in this paper, which achieves substantial gains over conventional algorithms. In the mean time, the maximal transmission capacity is not only related to the optimal access rate, but also to the system specific parameters such as Femto UE transmit power, target SIR and outage rate. Tuning these parameters enables the system to accommodate more number of FBSs simultaneously. Finally, the second-tier outage probability constraints are also derived, providing the optimal strategies for FBSs to maximize the second-tier throughput.