The 72-metre (240-foot) Esperanza was authorised to berth in an area of the port under supervision, a local official told AFP.
Greenpeace and other ecology groups are organising nationwide protests against the arrival of the plutonium which is to be recycled at a nuclear reprocessing facility at Cadarache, in southeastern France.
The ships, nicknamed "floating fortresses," left Charleston, South Carolina, earlier this month and are expected to arrive in Cherbourg around the end of the week.
A Greenpeace organiser said the Esperanza's objective was "to inform the public of the risks of this transfer (of plutonium) and of the development of this plutonium industry."