Barbara Weldens, 35, was singing in a church in the village of Gourdon, in the Lot region of southwest France, when she collapsed on Wednesday night.
The singer, who was one of the acts performing in the Leo Ferre festival, is reported to have suffered a cardiac arrest.
Some local media has suggested she may have been electrocuted, although this has not been confirmed.
Firemen who attended the scene were unable to resuscitate the singer.
A formal investigation has now been launched into the cause of her death.
Weldens, who grew up in a circus, was an accomplished acrobat, juggler and trapeze artist, performing with her parents before discovering her love of music as a teenager.
A talented musician, she also played the piano and acoustic guitar.
In 2016, she won first prize in the the Jacques Brel Young Talent Competition, and released her first studio album – with the tongue-in-cheek title Le Grand H De L’homme, which roughly translates as Man with a capital M – in February this year.
She was half way though a tour of France and Belgium, which she was due to finish at the end of October.