The two photos in the post show the same structure: Pulteney Weir, downstream of Pulteney Bridge on the River Avon in Bath. The shot of the "Seine" in Les Miserables was filmed on location in Bath.
Pulteney Weir was designed by architect Neville Conder, and built between 1968 and 1972. It's one component of the Bath Flood Prevention Scheme, which was carried out after the disastrous flood of December 1960. The Bath in Time website has photos of the old weir (which descended in a single step) and of the new weir under construction (1968, 1972).
An upstream view of the weir shows that there's more to the structure than the horseshoe-shaped steps: these meet a mid-river artificial island, and a channel to the left of the island terminates in a sluice gate.
(Photo by GeodesyMike from Wikimapia, licensed under CC-BY-SA.)
As with any weir, it has multiple purposes: to control the level of the river above the weir for navigation, fishing, and irrigation; to preserve water in long periods of drought; to hold flood waters back and release them gradually downstream; and to control the speed and force of the water, preventing the river from scouring the banks and damaging the foundations of the bridge and nearby buildings.
This video shows the weir in operation during flood. You can see that the shape of the weir directs the force of the water to the centre of the river, preventing it from damaging the banks.