Muffat had to draw on all her reserves of strength to win the gruelling eight-lap race as Schmitt, who trains alongside Michael Phelps in Baltimore, tried to reel her in.
Muffat timed her finish to perfection to get her hand on the wall first in four minutes, 01.45 seconds, an Olympic record, while Schmitt was second in 4:01.77.
Britain's Adlington, the Beijing champion, finished strongly to get the bronze in 4:03.11, giving the home nation their first medal in London's Aquatic Centre and eliciting a huge roar from the crowd.
Adlington was delighted despite her defence ending with a third place. Having squeezed into the final, the Mansfield-born swimmer had warned on Twitter: "Just sneaked into tonight's final in 8th place! Not expecting anything tonight, all I can do is my best :-) thank you for all the support x"
But after finishing her swim, she said: "The crowd was so overwhelming. Twelve years' hard work has gone into that."
"Four hundred metres always feel so hard for me and they were so far ahead. I'm so glad I've got a medal at a home Games. Not many people can say that."
Some of those packed into the Aquatics Centre, with its dipping roof like the underbelly of a whale floating over the pool, may have been disappointed at the colour of the medal after so much hype.
Adlington, the golden girl of British swimming and one of the few British swimmers with national recognition after her unexpected double gold medal haul in Beijing four years ago, was not one of them.
She was delighted, surprised and generally 'over the moon' to be the first Briton to medal in the home pool.
"I didn't even expect a medal, to be honest," she said, a comment that would have been entirely believable four years ago but that sounds much more surprising now.
"I'm happy to say I'm the third in the world."
Many others had expected more, however, with the blonde swimmer one of those expected to lead Britain's bid for more medals from more sports in more than a century.
"Another Olympic medal is just unbelievable and there's not an ounce of disappointment in me," she told reporters. "I gave it my absolute all and I'm so, so pleased."
Adlington had just scraped into the final, winning her heat but ending up with only the eighth fastest overall time.
Lane eight is never the best place to be to push for a medal but the setback also had a positive in taking off much of the pressure.
Adlington walked out, barely looking up so as not to be overwhelmed by the occasion, and splashed water on herself to cool down.
Sixth at the 150 metre mark, she was fifth by 250 and fourth at 300. At the turn for 350 she was in third place and the crowd was cranking up the volume by the second.
"I knew that those guys had been so good in the 400 all season, and for me my target always has been the 800," she said afterwards.
"I know after being in there that the 800 is going to be a battle and it's going to be hard work but it's nice to get the first out of the way."
She fed off the roar of the crowd, hardly a secret weapon given the level of noise but still a source of tremendous energy.
"That's what being at home is all about, it's what helped me secure that bronze medal," said Adlington.
"I heard the crowd, thought this is unbelievable, put my head down and went.
"I know some people will be, like: 'Oh, she only got a bronze' but swimming is one of the hardest sports to medal at...it is unbelievably difficult. I am so, so pleased.
"I know what I did in Beijing was great and I'll remember it forever but that doesn't mean to say I was going to come and win two golds here. Everyone else put that pressure and expectation on me. I didn't put that on myself."
The 800 is Adlington's more favourable event - she won it with a world record in Beijing and is the current world champion - and, even if some of her compatriots need a reality check, she will be a genuine contender for gold in that.
"I am going to have to fight like hell to get a medal," she said. "Hopefully the crowd can pick me up like it did tonight."
Meanwhile, Liam Tancock qualified for the final of the 100m backstroke after coming second in his semi-final behind Frenchman Camille Lacourt.
Robbie Renwick will also contest a final at the Aquatic Centre after coming third in his 200m freestyle semi-final behind Ryan Lochte of United States and Germany's Paul Biedermann.
Gemma Spofforth also helped make it a successful night for Britain when reaching the final of the women's 100m backstroke.
The world record holder was sixth fastest overall, and third in her semi-final, but team-mate Georgia Davies only came eighth in her semi-final.