Col Thierry Burkhard said French planes would transport military equipment to Kenyan soldiers near the Somali border.
But he denied Kenyan military claims that a French warship had shelled a Somali town on Saturday.
Meanwhile, some Somalis have protested against their president for opposing the incursion which began last week.
The several hundred protesters waved Kenyan flags and burnt pictures of President Sheikh Sharif Ahmed, the Reuters news agency reports.
The demonstrations took place in the border town of Dhobley and two other locations that Kenyan troops have passed through, Tabto and Qooqaani.
In Dhobley, protesters chanted “Down with Sheikh Sharif” and accused him of failing to understand the suffering caused by the militant Islamist group, al-Shabab, witnesses told the BBC’s Somali Service.
Kenyan motivesCol Burkhard said the French operation was “limited in scope”, the AP news agency reports.
It would see French planes helping the Kenyan army to transport military equipment from the capital, Nairobi, to an airport close to the Somali border, he said.
On Sunday, Kenyan army spokesman Maj Emmanuel Chirchir told the news agency that the French navy had bombed the town of Kuda along the Somali coast.
Col Burkhard denied the claim, saying France had no warships in the area.
Last week, al-Shabab lost control of the coastal town of Ras Kamboni after attacks by the Kenyan navy and a local militia.
Kenya sent troops into Somalia on 16 October to attack al-Shabab, saying it threatened its stability.
Nairobi accused the group of being behind a spate of kidnappings in Kenya, including that of a French woman, Marie Dedieu, on 1 October.
Mrs Dedieu, who had cancer, died in Somalia last week. Al-Shabab denied involvement in the abductions.
Nairobi said the deployment into Somali was done with the approval of President Ahmed’s government.
But on Monday Mr Ahmed said Kenyan support in terms of training and logistics was welcome but his government and the people of Somalia were opposed to the presence of the Kenyan army.
For more than two years, his weak UN-backed interim government has been battling al-Shabab, an al Qaeda-linked group which controls much of south and central Somalia.
His government relies on a 9,000-strong Africa Union force for its security in the capital, Mogadishu.
The BBC’s East Africa correspondent, Will Ross, says Mr Ahmed’s comments put the Kenyan government in a very difficult position.
It is possible that the Somali authorities have spoken out because they are opposed to the idea of Kenya helping to establish a semi-autonomous region in Somalia known as Jubaland, he says.
Al-Shabab has threatened reprisal attacks in Kenya if the troops do not leave. Kenyan police say two grenade attacks in Nairobi on Monday were not linked to the militant group.
Other foreigners being held in Somalia include a British woman abducted from a coastal resort and a Kenyan driver and two Spanish aid workers seized from the Dadaab refugee camp near the Kenya-Somalia border.