"On February 22, 2020 electric generating unit No1 at the Fessenheim power plant was disconnected permanently from the national power grid," the energy giant said in a statement.
The reactor is now being cooled before it can be opened to take out spent fuel. The second reactor will remain online until 30 June.
President Emmanuel Macron announced in November that his government would cut nuclear power production by half over the next 15 years under the green transition scheme.
The Environment Ministry has praised the first step to close the 43-year-old power plant as a "turning point" in the transition to renewable energy. But the trade union CGT representing the plant’s staff has lamented the reactor’s "death" on Twitter, saying their hearts were broken.