Hay's side kept working hard without the ball, keeping France at bay until the 32nd minute when Bilal Boutabba made it 2-0. Two minutes later France were 3-0 ahead as Emmanuel Maouassa struck before two goals inside the final five minutes of the half to Mamadou Doucoure and Alec Georgen made 5-0 at the break.
The second half saw the New Zealand side settle and an improved defensive effort restricted France to largely shots from outside the area.
That platform gave the New Zealand side more threat going forwards and Logan Rogerson had a great chance to pull a goal back in the 67th minute but scuffed his shot into the arms of France goalkeeper Luca Zidane - son of French legend Zinedine Zidane - after good work on the right flank by Lucas Imrie.
Woud was called into action immediately afterwards, making a superb save after a France break.
But despite that scare the New Zealand side continued to grow in confidence and they had their reward in the 76th minute when Rogerson charged down the left and into the area before cutting back to McGarry who drove home from six yards out.
New Zealand's next match is against Syria on Friday at 9am (NZ time) with LIVE coverage on SKY Sport 3.