Stravius clocked 1min 47.56sec, leading all the way to finish ahead of American Townley Haas (1:48.35) and fellow Frenchman Jordan Pothain (1:48.62).
Phelps, whose 22 Olympic medals include a staggering 18 gold, was third at the halfway mark, but couldn't mount a late challenge and finished off the podium in an event that featured among his eight gold medals at the 2008 Beijing Games.
While the 200 free is no longer a major focus for Phelps, he has been on the US 4x200m free relay team at the last three Olympics.
Among other finals on Saturday, the second day of the three-day meeting, freestyle phenomenon Katie Ledecky clocked a personal best of 1:54.43 to win the 200m freestyle -- improving on the 1:55.16 she swam to win the world title at Kazan, Russia last year.
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Sweden's Sarah Sjostrom, who had the fastest time in the world last year in the event but didn't race it at worlds, settled for silver in 1:56.14, with former world champion Missy Franklin third in 1:57.49.
Chase Kalisz was second in 4:14.64 and Josh Prenot third in 4:15.07 in a US sweep.
The women's 400m medley title went to Hungary's Katinka Hosszu, who cruised to victory in 4:36.27 after being shut out of the medals in the 100m free and 400m free on Friday.
Hosszu also captured silver in the 200m backstroke, won by American Maya DiRado in 2:08.19.
Hosszu clocked 2:08.63 and world record-holder Franklin was third in 2:09.21.
The 50 freestyles followed the formbook.
Sjostrom won the women's race in 24.17sec, adding the title to the 100m free gold she won on Friday with Madison Kennedy second in 24.72.