The wreck of the Mirage 2000-D was found near Mignovillard in the Jura region, at an altitude of about 1,000 metres (3,280 feet).
It vanished from radar during the morning on a low-altitude training flight, AFP news agency reports.
“We hope we’ll find them alive,” an air force spokesman said.
“At present they are reported missing.”
There has been no contact with the pilot and navigator since the jet vanished.
The air force spokesman, Col Cyrille Duvivier, added that there had been no ejection signal.
Commenting on a report that a parachute had been found among the wreckage, he said it was too early to tell whether it had belonged to a crew member or the plane itself.
The plane vanished from radar at around 11:00 local time (10:00 GMT), shortly after taking off from the Nancy-Ochey air base.
The area has received heavy snowfall in recent days which, along with low visibility, could make the search operation more difficult, officials said.
The plane is understood to have been unarmed during its flight.