The 60-year-old, who was acquitted in the first trial, has been chief executive of Orange for the past decade.
Bruno Le Maire, the French finance minister, stepped into the debate about Mr Richard’s role in the company. He has previously said that the government’s position was that chief executives in charge of state-backed firms must step down if convicted of a crime.
Orange, which is 27pc owned by the French state, held a board meeting on Wednesday where Mr Richard announced the decision to hand over his mandate.
He has previously said he would not seek to stay on when his third four-year term runs out in May 2022. However, he wanted to remain chairman.
The company’s directors said yesterday: “The Board thanks him for his commitment at the helm of Orange for the past 11 years, from restoring an appeased working environment after the social crisis to the transformation of Orange into a leading multi-service operator in Europe and Africa.”
“Stephane will have contributed significantly to the history of the group in sometimes tumultuous times and always working in the best interests of the company.”
The board added that it will continue the recruitment process started a few months ago to implement the new governance.
The case has no direct bearing on Orange’s business, which has expanded into the African market and diversified into online banking under Mr Richard.
Orange merged with rival operator T-Mobile in the UK 11 years ago to create the mobile network, EE, which BT bought for £12.5bn in 2015.
Orange has been struggling for growth as it grapples with the conflicting forces of needing to upgrade the network while facing fierce competition from rivals in France and Spain.
Profits slipped by 0.7pc to €3.6bn when it gave a third quarter update last month, despite French mobile and broadband customers rising by 121,000 and 80,000 respectively in the three months to September.
The company stood by its full-year targets, which included a slip in operating profit and underlying cash flow from €2.5bn last year to €2.2bn.
The Vodafone chief executive, Nick Read, has been pressuring European authorities to allow telecoms operators to consolidate as it battles anaemic growth in Italy, Spain and Portugal.