British rider Tom Pidcock was second after tailing Turgis but looked to be slightly blocked as he made a last-gasp bid for the line ahead of third-placed Derek Gee of Canada.
"That was wonderful," Turgis said at the finish line in the city of Troyes.
"I've been close to winning for ages and to get one here is just great," the 30-year-old added.
Overnight leader Tadej Pogacar attacked several times on a novel run including the dusty gravel for the first time on this race, but finished alongside his rivals for the title Remco Evenepoel and Jonas Vingegaard.
As France went to the urns in the second round of a parliamentary election hundreds of thousands of cycling fans turned out for the Tour on this first holiday weekend.
A shake-up in the overall standings had been expected as the peloton tackled 14 rustic white gravel paths in the region's celebrated champagne vineyards that produce over 300 million bottles of bubbly a year.
One of them was cracked open at the finish line by Turgis, who had been part of the long-range breakaway from a group of one-day specialists.
In the overall standings, the Slovenian two-time champion Pogacar leads Tour rookie Evenepoel of Belgium by 33 seconds while defending champion Vingegaard of Denmark is still third at one minute and 15 seconds.
