"I think Juppé is really the player to watch here, because Juppé has the ability to reach far into the political center and I think that is what is going to be required," Carsten Nickel, senior vice president at Teneo Intelligence, told CNBC.
Sarkozy, who was president between 2007 and 2012, announced his intention to run again via Facebook on Monday. He said he had "the strength to lead the fight at such a tormented moment in our history," in a post in French.
However, the former leader faces several competitors to be the presidential candidate for his center-right party. Some are not viewed as serious candidates, but others, such as Juppé and Francois Fillon, who was prime minister under Sarkozy, are.
France uses a two-round election system, which means that if no candidate received an absolute majority in the first round, all but the two leading candidates are eliminated and a second round of voting is held.
Juppé was prime minister under President Jacques Chirac between 1995 and 1997 and is currently mayor of Bordeaux. He is viewed as a unifying figure, unlike Sarkozy, who presided during the global financial crisis of 2007-08 and was charged with corruption in 2014. He is under investigation for suspected funding irregularities during his 2012 presidential campaign but denies wrongdoing.