She was performing at the Festival Leo Ferre in a small Roman Catholic church in Gourdon, a picturesque village perched high above the French Riviera.
The circumstances of her death are unclear and are being investigated by the local gendarmerie.
Ms. Weldens, who was in the habit of singing barefoot, suddenly collapsed in the midst of the performance and is believed to have suffered a cardiac arrest.
It is thought she may have stepped on a live cable.
Police are analyzing several videos taken by members of the audience on the night.
The Festival Leo Ferre, which was due to run until Friday (July 21) was immediately canceled as a mark of respect for the chanteuse.
[Tweet: "Our thoughts are with the family as well as the relatives of Barbara Weldens, deceased yesterday on the stage of the festival Leo Ferre"]
Weldens had produced her highly acclaimed debut album, Le Grand H de l'Homme, earlier this year.
Last year she won the Pic d'Or prize and the organizers of that competition issued a statement on Thursday (July 20).
"It was with great emotion that we learned this morning of the death of Barbara Weldens, our Pic d'Or 2016 at a concert last night in Gourdon in the Lot, obviously electrocuted. Our team is deeply disturbed by the brutal disappearance of the artist who had appeared on the stage of the Theater des Nouveaux on May 20, during our last edition. A radiant woman, full of energy and talented, and of course we think of all her family and her loved ones," they said.
Several famous musicians have been electrocuted on stage, including Keith Richards of the Rolling Stones and George Harrison of The Beatles, but it deaths are fortunately extremely rare.
In 2014 Nolberto, a singer from the Dominican Republic, fell into the crowd after receiving a massive electric shock on stage in Argentina.
He survived and even returned to the stage to complete his set.