The man was jumping off a cliff near the town of Petit-Bornand-les-Glières in the Haute-Savoie department of the French Alps.
The accident is believed to have taken place at around 8 pm on Wednesday evening, according to local press reports.
The exact circumstances of his death are unknown, mountain rescue teams reported, however it is presumed he was destabilised by trees after he made his jump in the mountainous area of rochers de Leschaux.
His body was quickly found by mountain rescue in a rocky area, local press reports stated.
He was accompanied by another Base jumper from the US and both were experienced in the extreme sport, which sees people jumping or wingsuit flying from a fixed structure, such as a building or bridge, or cliff edge, and plummeting towards the ground before opening a parachute.
It is not clear whether the victim was wearing a wingsuit or not.
The news was announced by the mountain rescue team in Annecy on Thursday morning.
On June 10th another BASE jumping enthusiast in his twenties died in the Drôme when the his parachute didn't open in time.
In 2016, the mayor of the French Alps town of Chamonix had banned the extreme sport of wingsuit flying for six months after a spate of deaths in the previous months.
The mayor said he was particularly worried for the safety of people in the town after a Russian wingsuit flyer crashed into a recently built châlet.
And that wasn't the first time the mayor of Chamonix had decided that a ban was the only way to cut the number of deaths.
Eric Fournier introduced a similar provisional ban back in 2012 after another spate of deaths.
“For us, adventure doesn't mean extreme risk. We have to ask questions of responsibility and respect for other sports,” he said at the time.