Perisic crossed for Ante Budimir to head in the opener at the Stadion Poljud in Split after the home side had squandered an early penalty.
With France out of sorts, Perisic made it 2-0 before the break and a Croatia side captained by Luka Modric saw out the victory to take to Paris for the return match on Sunday.
It was not a good night for France as captain Kylian Mbappe made his comeback having not featured in either of the last two international windows, in October and November.
Mbappe did have chances, notably seeing a deflected second-half shot from Ousmane Dembele’s cutback kept out by a fine Dominik Livakovic save.
The Real Madrid superstar has now failed to find the net in his last six appearances for his country, since scoring a penalty in a 1-1 draw with Poland at Euro 2024.
Les Bleus will now have to find a way of overturning the deficit at the Stade de France on Sunday, otherwise Croatia will be heading to the final four of the Nations League.
The semi-finals and final will take place in June and will be hosted by either Italy or Germany, depending on which of those sides emerges victorious from their last-eight encounter.
France won the Nations League in 2021 but suffered a first ever defeat against Croatia in the group stage of the following year’s edition.
This latest repeat of the 2018 World Cup final, won 4-2 by the French in Moscow, saw Croatia win a spot-kick just five minutes in.
Liverpool centre-back Ibrahima Konate was penalised for a blatant handball inside the area, but Mike Maignan saved Andrej Kramaric’s penalty after a long delay due to the goalkeeper having a laser pen shone in his eyes.
However, Croatia did get the breakthrough on 26 minutes as Budimir, who has 15 goals in La Liga this season for Osasuna, got in front of William Saliba to connect with a Perisic cross from the left.
Budimir’e header was blocked by Maignan, but the ball still spun into the net in cruel fashion for the goalkeeper.
It was 2-0 in first-half stoppage time as Saliba blocked a shot by Martin Baturina, only for the ball to fall for PSV Eindhoven veteran Perisic to fire in.
France made changes, sending on Dayot Upamecano for Konate at the restart and later bringing on Bradley Barcola for Randal Kolo Muani and Michael Olise for Dembele.
The latter spent more time on the right flank after the break having previously been deployed more centrally.
However, they could not get a goal back and now face a daunting task in trying to recover the tie. (AFP)
