Frenchman Bardet, second overall in last year's Tour de France, fell off his bike with about 23 kilometres 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-La Mondiale 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 Tour of Spain (Vuelta) after he also held onto his team car to make up lost ground.
The wind-hit stage was won by France's Arnaud Demare as Alberto Contador's chances of winning a third Paris-Nice title took a hit when he fell behind his main rivals.
The twice Tour de France champion was trapped behind with Australian Richie Porte and Bardet when crosswinds split the peloton and he lost further ground in the finale.
Contador (Trek Segafredo) lies 20th overall, 1:14 behind Demare, who beat compatriot Julian Alaphilippe in a two-man sprint at the end of the 148.5-km 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, Ireland's Dan Martin (Quick Step Floors) and Colombian Sergio Henao (Team Sky) are 19 seconds off the pace.
Porte (BMC), winner in 2013 and 2015, lies 57 seconds behind Demare.
(Reporting by Julien Pretot; Editing by Toby Davis)
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