Agnel was ruled to have finished third at the French championships, which served as the Olympic trials, after he failed to touch the pad correctly in the final.
Only the first two finishers could qualify for the Rio Games and Jeremy Stravius won the race ahead of Jordan Pothain.
Stravius is almost guaranteed a place despite missing the FFN's mark of 1:46.06 but his time 1:46.18 should be enough for the federation to include him in the preliminary selection it will unveil on Wednesday.
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Pothain is unlikely to be included.
Agnel thought he had finished second in Montpellier but the event's jury rejected his appeal because it is not allowed to watch TV footage.
The FFN, however, is hoping he will be able to defend his title.
"We will try to find something for him to post a good time. We have to do it," FFN technical director Jacques Favre told L'Equipe on Friday.
According to the FFN regulations, Agnel could still take part in the 200 metres freestyle if he beats Pothain -- and the time his team mate clocked on Wednesday -- before the Olympics.
One competition where Agnel could do it is at the May 16-22 European championships in London, where he won the Olympic gold medal four years ago.
(Reporting by Julien Pretot; Editing by Ed Osmond)
