This study investigates flood-induced dynamic responses of bridge piers and local scour around pile-group foundations, using the Jangwani Bridge in Tanzania as a case study. Separate fluid–structure interaction and coupled hydrodynamic–sediment transport scour models were developed for the bridge pier and pile-group foundation, respectively, to examine hydrodynamic forces, displacements, stresses, and scour evolution under different pier cross sections, approach-flow velocities, water levels, and pile diameters. The results show that the short-duration hydrodynamic response of bridge piers to the initial flood impact is distinctly transient and comprises three stages: initial impact, damped oscillation, and quasi-steady flow-past response. Under representative conditions, the peak transient impact force is 1.61–2.93 times the quasi-steady hydrodynamic load. Pier cross-sectional shape significantly affects the structural response, with the circular section exhibiting lower peak impact force and maximum principal stress than the square and rectangular sections. The fluid–structure interaction coefficient ranges from 0.98 to 1.41, indicating that the mean force predicted with fluid–structure interaction exceeds that for a rigid pier in most cases. Local scour around pile-group foundations develops rapidly at first, followed by slower growth toward the end of the 3000 s simulations. The scour hole is concentrated mainly near the upstream front-row piles, whereas the downstream rear-row piles experience less scour because of shielding. Under the selected reference condition and local perturbations, approach-flow velocity has the greatest effect on maximum scour depth, followed by water level and pile diameter. These findings provide a basis for flood-resilient bridge-substructure design, foundation scour protection, and construction-stage safety management in floodplains.