Argentina keeper Emiliano Martinez saved Kingsley Coman's penalty and Aurelien Tchouameni fired wide to give Argentina their first world title since 1986, and third overall.
France had come from two goals down to level over 90 minutes with Kylian Mbappe netting twice in two minutes, including an 80th-minute penalty.
The France striker completed his hat-trick in the 118th with another spot-kick after Argentina's Lionel Messi had tapped in for a 3-2 lead in the 109th.
Argentina had gone 2-0 up in the first half with Messi, making a record-breaking 26th World Cup appearance, converting a 23rd-minute penalty.
They struck again with a sublime four-pass counter-attack as Alexis Mac Allister's cutback found Angel Di Maria and he finished well.
Thousands of Argentina fans in blue and white outnumbered the handful of French supporters, creating an electric atmosphere and effectively converting the Lusail Stadium into a home game for Lionel Scaloni's side.
Messi, 35, became the first man in World Cup history to score goals in the group stage, Round of 16, quarterfinals, semifinals and final.
It's Messi's first World Cup title and he was named player of the tournament, while Mbappe won the golden boot with eight goals to Messi's seven.