Bouet pushed on solo, riding on home roads and with places in Etixx-QuickStep’s Tour de France squad up for grabs, but the peloton continued to ramp up the tempo.
BMC Racing hit the front, with Richie Porte’s GC ambitions and Greg van Avermaet’s stage hopes in mind but there was plenty of company – not least from Nacer Bouhanni’s Cofidis team-mates.
Bouet held on for as long as possible, before team-mate Tony Martin led the peloton past him with a congratulatory pat on the back for his efforts.
Giant-Alpecin were next to line-out at the very front – a clear indication of John Degenkolb’s belief his form is coming back – and a nasty crash in the bunch for a Cofidis rider didn’t halt the momentum.
The crash, fortunately, only directly affected one more rider as Giant-Alpecin continued to set a furious pace with plenty of passengers latched on behind.
It was Boasson Hagen who led the sprint out, however, picking a perfect line down the middle of the final straight.
Bouhanni tried to go round the outside, while Alaphilippe – in the white jersey – targeted bonus seconds as he made a move on the Norwegian’s inside.
Boasson Hagen would not be stopped, however, grabbing the stage win and the green jersey in the process.
Alaphilippe gained six bonus seconds in second place to buoy his own GC ambitions, meanwhile, as attention now turns to the mountains and the battle for the yellow jersey.
And there will be just four seconds separating Contador from Chris Froome (Team Sky), who was the right side of the gaps that appeared at the end to move into second place overall.