The two sides played out a dour goalless draw over 120 minutes of Saturday night's final in Istanbul, resulting in a penalty shootout.
And it was Paris Saint-Germain goalkeeper Alphonse Areola who emerged as the hero, saving spot-kicks from Emiliano Velazquez and Giorgian De Arrascaeta.
Les Bleuets netted all their penalties, with Dimitri Foulquier stepping forward to score the winning effort as the shootout ended 4-1.
Afterwards, Juventus midfielder Paul Pogba was named Player of the Tournament, picking up the Golden Ball prize.
Earlier at the same venue, Ghana beat Iraq 3-0 in the third-place match. Ebenezer Assifuah scored their second goal - his sixth of the tournament - to ensure he would claim the Golden Boot award for top scorer.