PARIS — As Syria began to descend into a bloody civil war, a cement plant in the embattled northeast run by one of France’s largest industrial companies was operating at full speed.

While fighting among Syrian rebels, the Syrian army and the Islamic State drove other foreign companies out of the country, the plant, operated by Lafarge S.A., was curiously able to tough it out for years: From its opening in 2010 through to 2014, cement continued to pour from its mills in Jalabiyeh, a town near the Turkish border.

On Monday, the company announced that its chief executive, Eric Olsen, would resign after an internal investigation that concluded last month found the Syrian operation’s managers paid off armed groups to allow safe passage for employees and keep supplies flowing to the multimillion-euro factory.

The group, now the world’s largest cement maker after a 2016 merger with a Swiss rival, Holcim, said it concluded that Mr. Olsen was not responsible for or aware of the activity. The group’s board has put him in charge of overseeing remedial measures and examining internal policies and financial controls to guard against future “misconduct” at any of its operations before he steps down in July.