Yannick Agnel clocked 48.02 seconds, a personal and French best this season, to win ahead of Fabien Gilot, fifth in last year's world championships, who finished in 48.38 seconds.
They both qualified for the Olympics with times below the required 48.82 but were much slower than the 47.10 set by world champion James Magnussen last week in the Australian trials.
The 28-year-old Bernard clocked 48.97, slower than the time he set in the semi-finals on Wednesday.
The Beijing Olympic champion had been banking on his experience to help him qualify after he failed to make the team for the world championships in the 100 metres last year.
But, just as he did in 2011 when he won a silver medal in the 50 metres at the worlds, he will now have to rely on that distance to qualify for an individual race at the Games.
"It's tough but I did not swim fast enough. It's part of the game. I am disappointed because I was thinking I could do much better and I did not. I still have the 50 metres and the relay," said Bernard.
William Meynard, the 2011 world 100 metres bronze medallist, did not even qualify for Thursday's national final.
Agnel, 19, had already booked a place in the 200 metres freestyle on Tuesday when he set a French record and world season's best of 1:44.42.
"My legs were a little heavy this morning, I was a bit tense. It's only happiness, it's really great. I'm satisfied but there is still a lot of work to do regarding the Australians," Agnel said.
"I am a little sad for Alain but he will be part of the relay. Water has flowed under the bridge in the last four years."
They will all be part of the six-man Olympic team for the 4x100m relay.