A coalition of France’s left-wing parties on Tuesday tapped a little-known civil servant to be prime minister, unexpectedly ending weeks of bickering after snap parliamentary elections plunged the country into political gridlock.

But President Emmanuel Macron immediately rejected the coalition’s pick, Lucie Castets. In his first interview since the elections, Mr. Macron said that he would not appoint a new government until mid-August at the earliest, and that his current cabinet would remain in a caretaker capacity for the duration of the Paris Summer Olympics, which start this week.

The French president alone has the power to appoint the prime minister and the cabinet. His choice must, theoretically, reflect the political balance in Parliament, but there is no constitutionally mandated deadline for him to choose.

The left-wing coalition, known as the New Popular Front, said in a statement that it had agreed on Ms. Castets, 37, who has worked at France’s treasury and its anti-money-laundering unit and currently handles financial matters at Paris City Hall.

“We will stand fully by her side in the government that she will lead,” said the New Popular Front, which won the most seats in the snap elections this month for the National Assembly, France’s lower and more powerful house of Parliament.

Ms. Castets graduated from the elite École Nationale d’Administration, which for generations has churned out top civil servants, and she is an active member of an association of civil servants that has opposed Mr. Macron’s policies.