Antoine Griezmann pounced on defensive confusion soon after and toe poked an effort goalwards, but Patricio was able to hold onto the shot on this occasion.
The home side had a slice of fortune in the 11th minute, though, as Danny blazed a shot high into the Stade de France stands after being released inside the box by a quickly-taken Cristiano Ronaldo throw in.
France found joy time and again down the right flank, and the Portugal defence were forced into a number of last-ditch clearances throughout the half, while Benzema hesitated on the ball and wasted a good opportunity on the stroke of the break.
Portugal reminded the home side of their attacking prowess and almost levelled in the 21st minute when Nani intercepted the ball after hesitation from Yohan Cabaye and Eliaquim Mangala, but the winger's low shot rolled narrowly wide of the far post.
Pepe almost inadvertently looped a header into his own net from a deep free kick, but Patricio was alert to tip the falling ball over the bar shortly before the break.
Ronaldo was denied an equaliser a few moments after the restart as Steve Mandanda dived low to his right to keep out the Real Madrid star's towering far-post header.
Portugal looked a more positive side in the second period, but Ronaldo cut an isolated figure in a central role.
Just as the visitors looked to be finding a foothold in the game, France doubled their lead.
The goal deflated Portugal, and, a few minutes after Pogba's strike, Blaise Matuidi saw his shot curl inches wide of the far post following a powerful run through the heart of the away side's defence.
Ronaldo was left frustrated as his goalbound volley deflected marginally wide via his Madrid teammate Raphael Varane, and the Ballon d'Or winner was withdrawn seconds later.
Fernando Santos's side were handed a lifeline 13 minutes from time when Pogba clipped the heels of Joao Mario inside the box, and Ricardo Quaresma stepped up to send Mandanda the wrong way from the spot, but France held on the secure the win despite a few late scares.