The hosts built on their overnight lead to lift the trophy for the first time in 16 years in front of 27,000 spectators at the Pierre Mauroy Stadium in Lille.
That set up a decider between Pouille and 76th-in-the-world Darcis, which the former eased through with a 6-3 6-1 6-0 triumph.
Speaking after the final match, Pouille said: "When Jo lost I was crazy in my head and I was like 'go on, play your game, try to beat him'. This is a feeling from another world.
"There are no words needed, just look at the atmosphere and hear the emotion right now. I am so proud of my team, we really wanted this trophy. After 16 years, we finally got it, I'm very happy."
France had previously lost their last three final appearances, coming in 2002, 2010 and 2014.