The plane went down at 9pm Tuesday near its air base on the outskirts of the city of Nancy.
During a press briefing from Doha, where he is on a visit, President Emmanuel Macron on Wednesday expressed "the nation's condolences".
Neither the pilot, aged 27, nor his 44-year-old navigator had time to eject before hitting the ground, Metz prosecutor David Touvet told AFP on Wednesday evening.
The motors from the ejection seats were found at the scene of the crash.
"Given the violence of the impact, no element of the investigation allows us to think that either of the two crew members will be found alive," Touvet stressed.
DNA analyses, which could take several weeks, will have to be carried out to identify the victims, he said.
The crew comprised "a highly experienced navigator and a young pilot who arrived at the base with all the prerequisites and qualifications needed to fly" a Mirage, Ludovic Humbert, the commander of the air base said.
"The pilot had 450 flight hours," Colonel David Pappalardo, spokesman for the Air and Space Force (AAE), told reporters in Paris.
He was "in the process of qualifying as an operational combat pilot", he said.
"At the end of the tactical phase of the training exercise, during the return at night, flying on instruments, air traffic control lost radio and radar contact," Pappalardo said, adding there was no distress signal and "no attempt to eject".
"With my husband, we felt the walls of our house shake a little before 11pm. We heard a kind of loud bang, like when an aircraft breaks the sound barrier, but worse," nearby resident Sandra Rotatinti told AFP.
Although they saw nothing, their neighbour, who was out walking his dog at the time, saw "a ball of fire in the sky" and called the fire brigade.
The plane crashed in a wooded area.
The two-seater Mirage 2000D model of fighter jet entered service in 1993. France has used it in conflicts in Kosovo in 1999, Libya in 2011, in Afghanistan, in Iraq, in Syria and in Africa's Sahel region.
Several have had accidents. In January 2019, both crew members aboard one making a low-altitude night flight died in eastern France. In July 2021 the crew of another was able to eject when their aircraft went down near Nancy.
France has just completed a renovation programme for its fleet of Mirage 2000Ds, which it intends to keep in service into the 2030s.
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