Sky teammate Geraint Thomas is second over all, 43 seconds behind van Avermaet, meaning the team has two viable options to claim the yellow jersey over the second week of the three-week Tour.
Julian Alaphilippe, a French rider for Quick-Step, won the 158.5km ride from Lake Annecy that included four major climbs before a descent to Le Grand-Bornand in 4 1/2 hours.
"I did not expect this, it's incredible", said the 26-year-old Alaphilippe after his first win on the Tour.
Sky have insisted Froome remains their team leader but also say that Thomas is allowed to race for himself in the early stages of the Tour.
Cavendish has 30 career Tour stage wins, four shy of Eddy Merckx's record, but it is now almost two years since his last.
The BMC team leader broke his collarbone and pelvis in last year's crash and was faced with the same decision to abandon after today's crash.
France's Romain Bardet, who was third overall a year ago, suffered three punctures but managed to limit the damage, only losing seven seconds to Froome and the four-time champion's Sky team mate Geraint Thomas.
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A day after the first rest day, the big guns were in no mood to take risks ahead of two more stages in the Alps.
"I'm going to try and ride tomorrow but obviously it's going to be very sore", said Martin at his UAE Team Emirates bus.
While the Dutchman followed up Friday's success in Chartres with a Bastille Day victory in Amiens on stage eight, Cavendish could enjoy a respite from questions over his form as there was little he could have done differently this time.
Van Avermaet won the single-day cobblestone Paris-Roubaix race in 2017.
Alaphilippe got his first Tour win after he attacked on the third ascent up the category-one Col de Romme and increased his lead over the Col de la Colombiere before the final downhill finish.
He joined an 18-strong break that had moved seven minutes clear by the time they crested the summit of the Montee du plateau des Glieres, heading on to the gravel roads over the plateau made famous by the French resistance in World War II.