We consider time and frequency-packed (TFP) multicarrier faster-than-Nyquist (MFTN) transmission that realizes non-orthogonal linear modulation to achieve higher spectral efficiency (SE) compared to the well-known orthogonal transmission at Nyquist rate. Such SE benefits come at the price of intersymbol interference (ISI) and inter-carrier interference (ICI), which usually are equalized through computationally demanding receiver-side processing. In this paper, we investigate an alternative approach of pre-equalizing the interference at the transmitter, for the first time in an MFTN system where symbols are packed in both time and frequency dimensions. First, we present a two-dimensional linear precoding technique to jointly mitigate the ISI and ICI at the transmitter. Second, we propose a partial precoding strategy to pre-equalize the ISI at the transmitter, while ICI being compensated at the receiver through an iterative interference cancellation method. We validate the flexibility of our designs by simulating a precoded coherent optical fiber communication system, as a practical application example for MFTN. Our numerical results confirm significant performance and complexity advantages of the proposed precoding schemes over existing interference mitigation approaches.