Agnel posted the third best time of 1min 46.99sec, putting him behind compatriots Jeremy Stravius and Jordan Pothain, who clocked 1:46.18 and 1:46.81 respectively.
Television images, however, appeared to show that the 23-year touched the wall in second, leading his coach Lionel Horter to launch a protest.
This was dismissed by the race jury almost two hours after the race and Agnel is now expected to appeal to the French National Olympic and Sports Committee
"For me I was second, it was quite clear," Agnel told reporters.
"Everyone I have met said I had evidently touched second, by quite a distance, and that there was no doubt.
"I believe their word."
Still images taken below the surface of the water appear to show Agnel touching the wall beneath the position of the touchpad, providing a possible explanation for the discrepancy.
"This problem has never happened to me and certainly never in the Olympic trials," added Agnel.
"It is a drama fit for the Olympic trials."
Neither Starvius nor Pothain managed to clock the minimum time of 1:46.06 set by the French Swimming Federation for automatic Olympic selection.
As the top two finishers, however, they can still make the cut through their placings.
The French Swimming Federation's Olympic qualifying standards are higher than the official cut-offs requested by the International Swimming Federation.
Stravius' time was the fourth best in the world this season, while Agnel's third-placed effort puts him in the top 10.
Agnel could still earn a place at Rio 2016 if he is selected on the relay team.
As well as winning 200m freestyle gold at London 2012, Agnel was also part of France’s 4x100m freestyle and 4x200m teams which won the gold and silver medals.
Both he and Hungary's Katinka Hosszu were named the European Swimming Federation's (LEN) European Swimmers of the Year in 2013.
The year saw Agnel lead France to its first ever global crown in the 4x100m freestlye event, beating the United States and Russia at the World Championships in Barcelona.
He then added a second gold medal in the 200m freestyle, beating his American training partner Conor Dwyer by more than a second.