TheLocal.fr reported one crew member of the Luno, a Spanish-flagged vessel, may have been hurt.
The cargo ship, which was empty when it broke up in stormy seas off southwestern France, apparently experienced engine failure, causing it to slam into the rock seawall.
Authorities ordered clean-up teams to the scene to remove leaking diesel fuel, TheLocal.fr said.
Mayor Jean Espilondo questioned why the ship had been given permission to head into the harbor in bad weather.
"We know that the entry conditions for the port of Bayonne are very difficult," he said.