This "white election" is the third in a row among the Immortals, after those of May and November 2022.
Mr. Neuhoff, 66, also a journalist and film critic, got 12 votes in the first and third rounds, and 11 in the second and fourth.
However, he needed 13 to gather an absolute majority.
Other candidates, the poet Alain Borer obtained five or six votes depending on the rounds and Jean-Yves Gerlat, an amateur of occult sciences, one in the first round then zero.
The election was marked by whites and "whites marked with a cross", between 8 and 11 per round.
The chair that remains vacant is number 19, previously occupied by the writer Jean-Loup Dabadie, but also Boileau, Chateaubriand, Paul Deschanel or René Clair.
Two journalists, Franz-Olivier Giesbert and Olivier Barrot, were initially rejected, not exceeding respectively 11 and 6 votes.
Then there were two writers, Benoît Duteurtre and Frédéric Beigbeder, with at best 11 and 9 votes.
Of the 40 chairs of the French Academy, five are to be filled to date.
The latest elected were the Peruvian-Spanish Mario Vargas Llosa, Nobel Prize for Literature 2010, and the academic Antoine Compagnon, in November 2021 and February 2022.
The election to the French Academy allows him to sit until the end of his days in an assembly founded in 1635 with the mission of defending the French language and writing a dictionary.
Despite the notorious difficulties in finding worthy candidates, the academicians have not lowered their level of requirements.
Mr. Neuhoff has indeed obtained from the Academy the Grand Prize for the novel in 2001 for "A crazy good" and the Grand Prize for literature Paul-Morand, for all of his work, in 2022.
Candidates who fail can try their luck as many times as they wish, which Émile Zola did 25 times, but which is not very recommended.
© 2023 AFP