PARIS—French President Emmanuel Macron formally announced Thursday that he will run for a second term in April’s presidential election, ahead of which he is already leading in the polls. In a “letter to the French” published on domestic media websites, Macron said: “I am seeking your trust again. I am a candidate to invent with you, faced with the century’s challenges, a French and European singular response.” Macron, 44, had long indicated that he wanted to run in the election, scheduled to be held in two rounds on April 10 and April 24, without formally announcing it until now. But his initial campaign plans have changed since Russia’s invasion of Ukraine. In the past weeks, Macron has dedicated most of his time to diplomatic talks with world leaders and coordination with European and other Western allies. Conservative candidate Valérie Pécresse and two right-wing figures, Marine le Pen and Eric Zemmour, …