We investigate the influence of the neutron halo and the breakup channel in He + U fusion at near-barrier energies. To include static effects of the 2n-halo in He nuclei, we use a single-folding potential obtained from an appropriate nucleon-U interaction and a realistic He density. Dynamical effects arising from the breakup process are then included through coupledchannel calculations. These calculations suggest that static effects dominate the cross section at energies above the Coulomb barrier, while the sub-barrier fusion cross section appears to be determined by coupling to the breakup channel. This last conclusion is uncertain due to the procedure employed to measure the fusion cross-section.