The man died after jumping off the 2,525 metre-high (over 8,000-feet) summit of Le Brevent in the French Alps.
"When his flying companion reached the ground, he realised something had gone wrong. He probably crashed into" the mountain, a rescue worker said, confirming the soldier's death.
His body was later found at an altitude of 2,100 metres. An investigation into the accident has been opened.
American daredevil Johnny Strange died in the Swiss Alps in October while also attempting a jump in a wingsuit.
The average wingsuit jump lasts barely a minute and within eight seconds, the jumper reaches speeds of 200 kilometres (120 miles) per hour.