PARIS — In the age of Donald J. Trump, “Brexit” and the resurgent French far right, a thin, aging career politician with an ironic smile is being called — by him and his supporters — France’s best defense against raging global populism.

A first test for Alain Juppé, 71, comes Sunday as France’s mainstream center-right Republican party holds a primary ahead of next spring’s presidential election. Mr. Juppé is favored to come out on top, for now.

His ascendance is all the more improbable because, in a previous post, he was considered one of France’s most unpopular prime ministers ever. And he was once convicted in a Paris City Hall corruption scheme.

But the election of Mr. Trump has upended French politics and given new momentum to the far-right leader Marine Le Pen. As a result, mainstream conservatives are far from delighted.