Pre being omitted from France squads due to the ongoing case with Valbuena, Benzema had been whistled and booed at the Stade de France for over three years. It's true in part that the refusal to sing La Marseillaise (the French national anthem) had much to do with the speedy disaffection growth towards Karim Benzema, but it was his lack of goals for France which were the main factor and here we're talking about a period back in the day where he was still scoring prolifically for Real Madrid.
In France they were accusing him of being lazy and the reality of the matter and the manner in which Benzema plays can lead you to believe he is lazy. Infact he has many similarities with Arsenal and Germany's Mesut Özil in this sense because when you watch him live at the ground you do get the sense that he isn't all that bothered about things until the ball arrives at his feet. There is a big difference that has to be taken into account when comparing this particular detail with both Benzema and Özil, which is that one plays up front where you CAN (and most do) hang around and wait (Griezmann doesn't do this though) for the ball by maintaining yourself or searching for the most dangerous position by adjusting your runs in the expectancy of receiving the right ball to do damage whereas in Özil's case he's a midfielder and a midfielder that doesn't run and cover kilometres is a drag and a drain on his team for which they will suffer in major games.
Where am I going with this?
Well the reason I've added all that is because everything has a part to play in Benzema's slow decline and it has nothing to do with age in his case. All of these factors in many analysts opinions have suffocated his game and at the end of the day he is (or should be) a high end elite athlete... You can't play for clubs or survive at clubs of the stature of Real Madrid and be part of an obvious slow cooking decline. The reasons he's stayed at Real Madrid in recent years is (everyone is in agreement with it) because firstly he was the perfect worker and provider for Cristiano Ronaldo (Cristiano loves playing with him and he's been vocal about this) and then when Zinedine Zidane arrived as head coach, he has been protected because he's of Algerian decent which although sounding extreme, this is something that's well known especially after the leaked chat Zidane had with Álvaro Morata last summer before the young Spaniard made the decision to force his move elsewhere which ended up being Chelsea.
When you change your game so radically from one thing to another, you end up becoming that. Benzema is a technical forward, one that has great ball skills coupled with good body strength which has served him well during his younger years. But all of this messing around and becoming submissive whilst also adding his personal issues off the field has turned him into the current example we have which unfortunately isn't good enough for Real Madrid and also his national side, France (this, even without the Valbuena issue). Benzema is human, and as a human being when you do something for too long, it becomes part of your nature.