Witnesses in Bulo Marer said they had heard a helicopter above the southern town before explosions and gunfire.
Al-Shabab militants are believed to be holding a Frenchman hostage there.
An al-Shabab spokesman told AFP news agency “several” French soldiers had been killed, in a claim which could not be confirmed independently.
The reported operation in eastern Africa came hours after France announced the start of a military intervention in the west African state of Mali, to support the government there against Islamist militants.
It was not immediately clear if the two events were connected.
A French secret agent named as Denis Allex was kidnapped in Somalia in July 2009 along with a colleague who was freed the following month.
A Somali intelligence official, speaking on condition of anonymity to AP news agency, said French commandos had attacked the base in an apparent bid to rescue a foreign hostage.
Mohamed Ali, a resident of Bulo Marer, described the events of Friday night by phone.
“We heard a series of explosions followed by gunfire just seconds after a helicopter flew over the town,” he told AP.
“We don’t know exactly what happened but the place was an al-Shabab base and checkpoint.”
Another resident of the town, Idris Youssouf, told AFP that details were sketchy because the attack had happened at night.
“But this morning we saw several corpses including that of a white man,” he added.
He said three civilians had also died in the fighting.
According to the website Somali Memo, which is broadly supportive of al-Shabab, militants fought off the French commandos.
Following the fighting, the situation in the town was calm and the militants had brought in reinforcements, the website said.