The nuclear watchdog of Europe's biggest atomic energy nation said it had dispatched a team of experts to check the site in Romans-sur-Isere, but did not give any indication about the size of the leak.
Areva, a state-controlled company which makes nuclear reactors and deals with uranium, said the leak was confined to its FBFC site and did not pose a danger to the environment.
"The defective pipe was shut by our teams," Areva said in a statement, adding that the pipe linked a workshop making fuel to a uranium treatment station.
News of the leak came the day after France ordered tests at all its 19 nuclear power plants following the discovery that liquid containing non-enriched uranium had been accidentally released from another Areva site in southeast France.
Areva told the nuclear safety authority ASN that the latest leak came from a buried pipe transporting liquid uranium and that the crack in the tubing was "several years old".
"Areva will start the cleaning of the impacted zone on July 18," the ASN said in a statement, adding that the pipes did not appear to meet safety regulations.
Areva said it would ask the ASN to classify the leak at level one of the International Nuclear Event Scale, used to measure the potential danger of incidents at nuclear sites. The scale has seven levels, the lowest of which is zero.
The ASN criticized Areva for the way it handled the previous leak at Tricastin, which was also classified as a level one event, saying it delayed communication of the problem and had unsatisfactory security measures in place.
Areva has since named a new manager for the Tricastin plant who has been told to review procedures at the site.
News of the latest incident is a fresh embarrassment for Areva which is at the forefront of French President Nicolas Sarkozy's effort to sell home-grown nuclear energy technology to the rest of the world.
The problems could also cast fresh doubts on France's recent decision to build a second new-generation European Pressurised Reactor (EPR) by 2017, bringing to 60 the number of nuclear reactors in France.