Bardet, second overall in last year's Tour de France, fell with about 23km left and made his way back to a group of chasers by breaching the rules on team car assistance.
The disqualification is a blow for the AG2R rider as the week-long Paris-Nice race was an early goal ahead of July's Tour de France.
In 2015, Italian Vincenzo Nibali was disqualified from the Vuelta a Espana after he also held onto his team car to make up lost ground.
The wind-struck stage was won by Arnaud Demare as Alberto Contador's (Trek-Segafredo) chances of winning a third Paris-Nice title took a hit when he fell behind his main rivals.
The two-time Tour de France champion was trapped behind with Australian Richie Porte (BMC) and Bardet when crosswinds split the peloton and he lost further ground in the finale.
Contador (Trek Segafredo) lies 20th overall, 1min14sec behind Demare, who beat Julian Alaphilippe in a two-man sprint at the end of the 148.5km stage around Bois d'Arcy.
Alaphilippe (Quick Step Floors)attacked the leading pack on a short climb near the finish but Demare (FDJ) reined him in and easily won the sprint.
Among the favourites for the overall title, Dan Martin (Quick Step Floors) and Sergio Henao (Sky) are 19 seconds off the pace.
Porte (BMC), a winner in 2013 and 2015, lies 57 seconds behind Demare and is now well position for a repeat after the travails of Contador and Bardet.
"Clearly it was an eventful stage and I took great pleasure in being part of it," Demare said. "It was a crazy race with at the echelons. It was less cold than we expected but it was still a very hard race.
"We started to lead the chase and lead the tempo and then suddenly Lotto went up a gear as Tony Gallopin knew the terrain like the palm of his hand. The move surprised the rest of the field and the pack broke up.
"We were lucky to be in the front and there were suddenly six of us in the front. When Julian Alaphilippe attacked in the last kilometre, I knew I would beat him in a sprint but the hardest part was to stay with him in the bump."