They are reportedly analyzing several videos taken the night of the festival as part of the investigation.
Weldens released her first studio album, Le grand H de l'homme, earlier this year and had won a young talent award in 2016.
The singer, who grew up in the circus, was in the middle of a tour when she collapsed.
Following the singer's death, the Festival Léo Ferré was canceled.
Organisers of the Pic d'Or, gave Weldens a young talent award in 2016, released a statement, speaking of her energy and talent.
The statement said: "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 20th, 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."