Such was the furore that even the French government weighed in, seeing grounds for disqualification if David had tested positive.
France's Europe minister Clement Beaune had called for "total transparency".
"I think there needs to be no doubt here," he told RMC radio.
"If there is a problem, there are penalties... Provisions are made for sanctioning measures, including potential disqualification in case of problems," he said.
French hopes had been riding high on singer Barbara Pravi, who was a bookmakers' favourite to end France's 44-year Eurovision drought with her moody ballad "Voila".
But she was edged out at the last minute by a surge in public votes for Måneskin.