PARIS, Sept 22 (Reuters) - Three Frenchmen working for marine services supplier Bourbon were kidnapped off the coast of Nigeria on Wednesday, just a week after the abduction of five French nationals in neighbouring Niger.

French Defence Minister Herve Morin said the overnight kidnapping in Nigeria, where several speed boats attacked a vessel owned by French marine services company Bourbon GPBN.PA in the oil-rich Gulf of Guinea, appeared to be the work of pirates.

The other 13 crew members were unharmed, the company said.

Morin insisted, however, that France had received warnings of a heightened terror threat from several intelligence services following the abduction of five French nationals in the lawless uranium-rich northern region of Niger last week.

Al Qaeda's North African wing (AQIM) claimed responsibility on Tuesday for the kidnapping of the five French nationals and two other foreigners working for French nuclear firm Areva CEPFi.PA and construction group Vinci SGEF.PA , marking an escalation between the group and France.

"The Gulf of Guinea is rife with pirates ... and everthing suggests this was an act of piracy," Morin told France 24 TV."But the terrorist threat is a real threat."

Morin said there was every reason to believe the claim of responsibility for last week's kidnapping by AQIM, which executed a 78-year-old French hostage Michel Germaneau in July when a French-Mauritanian raid to free him failed.

France announced a heightened alert for possible terror attacks this week after receiving a tip-off that a female suicide bomber was planning to attack Paris' metro system.

"The terrorist threat exists and we had information from a certain number of foreign services saying that France was the object of a particular threat," Morin said.

NO CLAIM OF RESPONSIBILITY

Bourbon, which is working closely with French and Nigerian authorities to investigate Wednesday's attack, said no claim of responsibility had been made at this stage. Nigerian authorities said they were investigating the incident.

Kidnappings are frequent in the Niger Delta area of eastern Nigeria, the heartland of Africa's biggest oil and gas industry which is often targeted by criminal gangs and insurgents calling for greater regional autonomy.

"There is no link between the Bourbon employees and the five French hostages in Niger, because the Niger Delta population in Nigeria are in conflict for regional reasons," said Philippe Vasset at Intelligence Online in Paris.

In 2008, 10 crew, including seven Frenchmen, were kidnapped on a Bourbon ship off Cameroon and freed 10 days later.

Before last week's attack, French authorities had said there were three foreign nationals being held overseas - two in Afghanistan and one in Somalia. These latest kidnappings would take that tally to 11.

"France is doing everything necessary to make sure that its citizens return home," Morin said, adding that intelligence units had been deployed in the region. He declined to comment on media reports a special force unit had been sent to West Africa.