I live in France, Sarkozy lost popularity due to:
He was not centrist enough, he tried to reform the trade unions and socialist tendency of France which is a very steep task, but he didn't improve the lobbying situation in France.
His child almost gained access to a corrupt job after college: Director of Trade in Paris Defense District (i.e. Mayor of New Jersey at 20 by official appointment) with an annual budget of more than 1 billion: https://en.wikipedia.org/wiki/Jean_Sarkozy#La_D.C3.A9fense_controversy
He was aggressive against Hollande in the national debate, and presented more of an upset, angry tirade, against Hollande's moderate, defensive, calmer stance.
https://www.youtube.com/watch?v=wm88_4pb3Qg (see for yourself who was more self assured, else read the behaviour analyses in the media from that time)
The same happened with the previous challenger, Segolene Royale, who was upset, angry, accusative towards Sarkozy in the previous election's televised debate, and she lost out.
Better alternatives to Sarkozy have emerged for the right: Francois Fillon is the previous Prime Minister under the President and has a calmer temperament and voice and is more centrist.
Sarkozy is impulsive, exciteable, has ticks, sometimes poor mannerism, sometimes slobbish expressions, lack of presidential grandeur. He had a tendency to be bombastic, imperial and agricultural, in a peculiar combination.(example of some behaviour that the media found to be brash: https://www.google.fr/search?espv=2&biw=896&bih=542&tbm=isch&sa=1&q=sarkozy+mauvaise+presentation ... if you want, compare with his challenger: https://www.google.fr/search?espv=2&biw=1024&bih=620&tbm=isch&sa=1&q=fillon+mauvaise+presentation)
Perhaps i can compare him to Tony Blair, both strongmen, Previously Sarkozy was popular because he was vociferous, energetic, educated and idealistic, with a good record in law and order, anti-immigration, but he didn't make it as a national reformer. Tony Blair did reforms on the national system in his clumsy but nationally reforming way. For example, Tony Blair achieved the peace deal with Ireland, the "Devolution of Parliaments" program and "Transparency of UK affairs", which changed the UK considerably, with Scotland having a parliament, and N. Ireland, rejuvenated the education system with the "New Deal" to make it easier to get paid apprenticeships for students, and had other big popular programs like "Cool Britannia" for international image, he also scrapped the previous industrial regulators for telecoms and pharmacy and rebuilt them, larguely because they were indemically corrupt in the UK.
Sarkozy did relatively little of that, He pushed in a lot of smaller reforms. No big programs, (you may cite HADOPI, one of his big branded programs, to stamp out web piracy, a failed Sarkozy venture.) no cool branding for his programs, I can't honestly say that i heard France gaining notable big reforms in the 9 years i lived here, other than contentious laws against socialist rights and worker rights. That said, France didn't have the endemic corruption problems in all industries that the UK did after John Major and the Thatcherite movement, so there was less reforming to do in France.
France gained in wealth due to it's cautious banking, but is much the same as it was, very socialist with a lot of free education and a very slow monolithic national government which has trouble making decisions, but that is less likely to have rogue subversive governments like Thatcher's ended up, and Bush's was. France is inefficient in some ways and used to have a larger middle class because of less of the 1% phenomenon by providing for the poor and taxing the industries. As long as the population aren't treated unjustly in France, their political will is not that passionate.
Like in most big governments, France has a problem of Elitism in politics, all the leaders hail from the same academies and it's very difficult for an independent like gain popularity with the media moguls and be taken seriously by politicians. There is one thing for certain in French politics it's that Marion Maréchal-Le Pen is the hot one to look out for in ten years.