Last week, Sarkozy had announced that he would seek the leadership of the centre-right Union for a Popular Movement (UMP) party, BBC reported.
The development came after the suspension Wednesday of a case against Sarkozy about an alleged attempt to influence judges who were looking into his affairs.
Sarkozy denies all allegations against him.
“My dear friends, it is a long walk that we are starting in the service of France,” Sarkozy said.
“I have had time to think about what we did, and to you the people of France, I wanted to say thank you.”
He intends to contest the 2017 presidential election.
Sarkozy served as the 23rd president of France from May 16, 2007 till May 15, 2012.