The heroes came from both ends of the pitch. The Scots goals were scored by Kenny Bain and Alan Forsyth, while Tommy Alexander saved from the spot to deny the French.
The Scots got their noses in front a couple of minutes before the break when a cross by Jamie Wong was brilliantly deflected into the net by Bain.
The French put the Scots defence under considerable pressure in the second half but in a rare breakaway the hosts sneaked a second. Lee Morton released the ball to Gordon McIntyre who drew the goalkeeper, leaving Forsyth with the simple task of rolling the ball home.
In the final quarter Chris Grassick was adjudged to have pushed a French forward but Alexander pulled off a brilliant save by from the spot.
Simon Martin Brisac eventually pulled one back for the favourites but the Scots were not to be denied.
Earlier in the day Ukraine marched to the top of the pool with a 7-2 thumping of Portugal.