The Real Madrid striker netted twice in two minutes after the break, adding to Antoine Griezmann and Yohan Cabaye's goals, before being substituted with less than 10 minutes left due to a thigh problem.
It was France's third victory in a row after the Euro 2016 hosts beat Serbia and Portugal in friendlies last month.
They next face Denmark in Copenhagen and once again they will be without midfielder Paul Pogba who was ruled out of Thursday's game in Nice and will also sit out Sunday's match because of a sprained ankle.
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As expected, it was a one-sided affair at the Allianz Riviera.
Mathieu Valbuena and Griezmann were the most dangerous France players, threatening the Armenia defence on the flanks.
Griezmann opened the scoring 10 minutes before the interval, firing home a powerful low shot from just outside the box after a fine one-two with Benzema.
France went 2-0 up 10 minutes into the second half when Cabaye was set up by Valbuena and curled a perfect shot into the far corner.
Benzema made it 3-0 with a header from Griezmann's corner in the 78th minute, just before rubbing salt into Armenia's wounds with a low shot after being set up by substitute Anthony Martial.
Benzema was replaced by Olivier Giroud two minutes later, holding his thigh as he limped off the pitch.
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