By Dominique Vidalon and Matthieu Protard PARIS (Reuters) -Societe Generale Chief Executive Frederic Oudea in a surprise move on Tuesday said he would not seek to renew his mandate at the next shareholders’ meeting on May 23, 2023. France’s third-biggest listed bank said it would launch the process of finding a successor for Oudea, who has been CEO since 2008, and should be finished by 2023. “It is a decision I took with humility, lots of emotion but also with a serene mind,” said Oudea, whose last major job was to broker an orderly exit from Russia through the sale of the company’s local unit…