There were hardly any fireworks in a cautious first half at the Stade De France with French President Emmanuel Macron in the stands.
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Nantes, beaten twice in the league by Nice this season, struck immediately after the restart with Blas smashing his 47th minute penalty into the roof of the net after Hicham Boudaoui's hand ball.
Nice, making their first final appearance since 1997, had ended Paris Saint-Germain's reign as Cup winners this season but struggled to break past the disciplined Nantes defence.
It was the fourth time Nantes, nearly relegated a year ago, won the title and the fourth for coach Antoine Kombouare, who had won two as a PSG player and one as PSG coach.