Abstract: We present an FPGA-based study of the acceleration of matrix-element computations for Monte Carlo event generation, using MadGraph5_aMC@NLO as a benchmark framework. Two complementary benchmarks are considered. First, we map the phase-space-generation and matrix-element-evaluation stages of the benchmark process e(+) e(-) -> mu(+) mu(-) onto an AMD Alveo U250 accelerator, enabling a compute-only assessment of the mapped FPGA pipeline. Second, for the more complex gg -> t (t) over bar + X processes with increasing jet multiplicity, we investigate FPGA acceleration of the colour-algebra kernels as structured targets for selective acceleration. In this second case, the reported speedups correspond to the isolated colour-reduction kernel operating on precomputed amplitudes, rather than to the full matrix-element evaluation or the complete event-generation workflow. The proposed implementations are developed using High-Level Synthesis and are evaluated in terms of numerical accuracy, performance, device-level energy efficiency, resource utilisation, and scalability. Under the stated compute-only measurement methodology, the FPGA implementations achieve substantial speedups and lower energy per event than the evaluated CPU and GPU baselines. For the considered benchmarks, the numerical results show good agreement on average with the corresponding CPU reference calculations, while the resource analysis highlights the importance of numerical representation in determining FPGA scalability. Taken together, these results demonstrate the potential of FPGAs for accelerating selected matrix-element and colour-algebra kernels, while further integrated evaluation is required to determine their end-to-end benefit within heterogeneous Monte Carlo event-generation workflows in high-energy physics.