Al-Jazeera shows images of al-Qaeda hostages in Niger
Two of the French nationals were employees of the French nuclear energy firm, Areva, which operates the mine near Arlit.
The other five hostages worked for a subsidiary of the French construction company, Vinci, which was a subcontractor there.
The hostages and their captors were last seen heading towards Inabangaret, an important well and stopping point in north-western Niger.
It is believed they are being held in the mountains of northern Mali.
In the images broadcast by al-Jazeera, the seven hostages are shown sitting cross-legged on sand with seven armed men standing behind them. The captors' faces are obscured by the turbans they are wearing.
The video featured them being asked in French about their names, ages, marital status, al-Jazeera said. When asked if they know the identity of their kidnappers, the hostages said they were members of al-Qaeda in the Islamic Maghreb (AQIM).
It is not clear when the footage, which has now been posted online, was filmed.
The French foreign ministry said the group photograph had been authenticated.
"Even if we don't know when it was taken, it's an encouraging sign in as much as it shows all the hostages alive," a statement said, according to the AFP news agency.
An audio statement by AQIM broadcast by al-Jazeera last week said a group led by Sheikh Abou Zaid - its leader in northern Mali - had managed to evade the tight security in place at Arlit and kidnapped "five French nuclear experts" on 16 September.
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 has sent 80 military personnel, as well as aircraft equipped with sophisticated monitoring equipment to Niger's capital, Niamey, to help search for them.
AQIM, a North African offshoot of al-Qaeda, 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 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.