The identity of the reporter and the organisation who employed the journalist were not released.
French authorities are in touch with "those who seem to be the kidnappers", Bernard Kouchner, the French foreign minister, told French television.
"I hope that the contact will not be lost and I hope that it only concerns a demand for ransom," he said.
Bossasso is the economic capital of Puntland and faces Yemen, across the Gulf of Aden, where many African illegal immigrants attempt the perilous journey in a bid to reach wealthy Arab nations.
However, some 300 people have died and a further 300 were reported missing last year, according to the United Nations High Commissioner for Refugees.
The Puntland region, although relatively free of the violence that has plagued the rest of the country, has become increasingly associated with kidnappings and piracy.