Once inside the plant at Fessenheim, in eastern France, the activists hung a banner reading "Stop risking Europe" on the side of one of its reactors "to denounce the risk of French nuclear power for the whole of Europe," the group said in a statement.
"These actions will not have any impact on the working of the plant which is functioning normally," said a spokesman for the state-run company EDF, which runs the facility.
Police had detained 56 activists, he said, but 20 remained on top of the dome of one of the reactors as a police helicopter hovered above.
France operates 58 reactors and is highly dependent on nuclear energy. It is one of the world’s leading exporters of non-military nuclear technology.
But in a deal with the Greens before the 2012 presidential elections, President Francois Hollande promised to cut reliance on nuclear energy for electricity from more than 75 percent to 50 percent, by shutting 24 reactors by 2025.
Hollande specifically pledged to close Fessenheim, which was commissioned in 1977, by the end of 2016.
The plant, on the banks of the Rhine, is close to the Swiss and German borders and is considered vulnerable to seismic activity and flooding.
The Greenpeace protest stunt comes ahead of a meeting by European leaders to discuss the future of the continent's energy policy.
Greenpeace wants Hollande and German Chancellor Angela Merkel to push Europe towards an energy transition. The group complains that France relies too much on nuclear energy, and Germany on coal, for electricity supplies.