Bugey nuclear power plant in Saint-Vulbas. AFP
Protest organisers said six people were badly hurt and about 30 lightly injured in the clash in Bure.
The local prefecture said that, according to calls to the emergency services, at least three demonstrators had been injured.
Two gendarmes were hurt by a “home-made device thrown by protestors”, the prefecture said.
Around 300 protestors took part in the demonstration, some of them helmeted and wielding stones, sticks and Molotov cocktails, the authorities said.
The rally was held to oppose plans to store highly radioactive waste 500 metres (1,640 feet) underground at a nearby site — the dangerous long-term by-product of France's extensive nuclear energy programme.
Debate over Bure has been raging for years, pitching France's vocal environmental lobby against its powerful nuclear industry.
In July, the National Agency for the Management of Radioactive Waste (ANDRA) said construction of the storage site would start in 2022 at the earliest.
But earlier this month, a national watchdog, the Nuclear Safety Authority (ASN), declared it had “reservations” about the project.
It cited uncertainty about how highly inflammable waste would respond if temperatures rose.