Van Avermaet had been present in all the major breaks of the day, including the final attack that saw Matteo Trentin (Etixx Quickstep) Tosh Van der Sande (Lotto Soudal), and the BMC Racing rider go clear.
The trio looked set to decide the race between themselves in an even sprint but with just over 1,300 metres to go Van Avermaet drifted to the back of the group and called for assistance. It was clear he had a problem and when Trentin started his race-wining sprint Van Avermaet was forced to sit up. Van der Sande took second with Van Avermaet drifting over the line in third.
"At first, I thought maybe I could still sprint because I did not flat directly," he said in a team statement. "But in the final corner, I felt it was going to be tricky. When they started sprinting, it was already totally flat and my race was over."
BMC Racing Team Sport Director Yvon Ledanois said there was no time to change the wheel.
"If we change the wheel, Greg doesn't get top three and he gets nothing. He was just not lucky. For sure, he had the legs to take the win today."
Van Avermaet, a winner in Paris Tours in 2011, had joined the main break of the day that included over 30 riders and his teammates Tom Bohli. It was Trentin who sparked the wining move with less than 10 kilometres to go with Van Avermaet, Van der Sande and Tinkoff Saxo’s Pavel Brut latching on. The Tinkoff rider was dropped on the final small climb.
"Everything before this mechanical problem, the team did well," Ledanois said. "Tom was with Greg in the breakaway and he did a good job for him. And Greg was there in the final. He just did not have good luck. C'est la vie. (That's life.)"