PARIS—Former Prime Minister Alain Juppé said Monday he won’t run in France’s presidential election, leaving his conservative party scrambling to unify behind the embattled primary winner, François Fillon.

Recent surveys have shown Mr. Fillon, the onetime favorite to become France’s next president, getting knocked out in the first round of voting on April 22. His campaign is reeling under an investigation into allegations that he arranged fake, government-paid jobs for his wife and two of his children.

Mr. Fillon, who has repeatedly denied wrongdoing, is scheduled to appear in court on March 15 to face preliminary charges.

Senior members in Mr. Fillon’s campaign team, some of whom are Mr. Juppé’s political allies, resigned last week. That fueled rumors that Mr. Juppé was positioning himself to succeed Mr. Fillon as the candidate of the center-right party, Les Républicains, after finishing second in the November primary.

Surveys in recent days showed that if he ran, Mr. Juppé would make it to the second round. But on Monday, he ended the speculation.

“I confirm once and for all that I will not be a candidate for the presidency,” he said from the southern city of Bordeaux, where he serves as mayor.

Party officials attempted to rekindle unity around Mr. Fillon at an emergency meeting Monday evening.

“The time has come for everyone to get a grip and be reasonable again,” Mr. Fillon told the officials.

Afterward, party secretary Bernard Accoyer said they were unified behind Mr. Fillon. “Les Républicains are in are in battle formation and have relaunched the campaign,” Mr. Accoyer said.

But the party faces a struggle after a bruising battle.

In his statement, Mr. Juppé slammed Mr. Fillon for criticizing the media and legal system over the handling of the investigation into the allegations. The candidate’s claims to be the victim of a political assassination have led him into an impasse, Mr. Juppé said.

Mr. Juppé, who campaigned on a centrist platform, said Mr. Fillon had driven out centrists and radicalized the party’s right-wing base. But he said he wasn’t in a position to rebuild party unity.

He also said his own record no longer measures up to heightened demands for politicians to be exemplary. In 2004, a court sentenced Mr. Juppé to one year of ineligibility for public office and a 14-month suspended prison term for his role in a fake jobs scandal at the Paris city hall.

After winning a resounding primary victory, Mr. Fillon looked set to win the election against a divided left and the National Front candidate, Marine Le Pen.

That advantage has been squandered, Mr. Juppé said.

Since the launch of the investigation into Mr. Fillon, polls indicate that Ms. Le Pen and Emmanuel Macron, leader of independent centrist party En Marche, will easily qualify in the first round for the runoff on May 7. Mr. Macron would win the head-to-head contest, the polls indicate.

Mr. Juppé said whoever represents the center-right in the presidential election will face the challenge of repairing a “sick” country, angry with its political elites and open to demagogic ideas.

“Our country is going through a terrible crisis of confidence,” Mr. Juppé said.