A ministry spokesman said France had no proof the five were alive but had "good reasons" to believe they were.
He said a claim from al-Qaeda in the Islamic Maghreb (AQIM) was genuine.
Another two people, one from Togo and and the other from Madagascar, were seized along with the French group.
Speaking to AFP news agency in Paris, foreign ministry spokesman Romain Nadal said the government was "in a position to confirm the authenticity of the claim" from AQIM, which was broadcast on the Arab satellite network al-Jazeera.
He said France had received no other communication and was not yet aware of any precise demands from the hostage-takers.
The AQIM statement said the group would issue demands to the French government "shortly" and warned against doing "anything stupid".
Niger's government believes the kidnappers are affiliated to Abou Zaid, the AQIM leader in northern Mali.
France has sent 80 military personnel to Niger's capital Niamey to help search for the hostages.
They are backed by a long-range Breguet Atlantique aircraft and a Mirage jet equipped with sophisticated monitoring equipment.
Two of the French nationals are employees of the French nuclear energy firm Areva, which operates the mine near Arlit.
The other five hostages work for a subsidiary of the French construction company Vinci, which is a subcontractor there.
The hostages and their captors were last seen heading towards Inabangaret, an important well and stopping point in north-western Niger.
The AQIM is active in the region and has kidnapped French and other European nationals in the past.
In July, the group announced that it had executed a 78-year-old retired French engineer it was holding hostage in Mali, after a raid by the French and Mauritanian armed forces had failed to free him.
The following month, the Spanish government is believed to have paid millions of euros to free two of its nationals seized by AQIM in Mauritania.
Niger is the world's sixth biggest producer of uranium, and the radioactive heavy metal is its main export. Areva gets much of its uranium from the two mines it operates in the country, Arlit and Imouraren.
France's foreign ministry has confirmed that an al-Qaeda group is holding five of its citizens after abducting them from a uranium mine in Niger.