A loss would have all but knocked the Scots out of the tournament, but Oliver Burke’s first-half strike proved enough to claim a valuable three points.
Scotland skipper Burke latched on to a long ball from Robby McCrorie in the first half and fired in from a tight angle through the hands of goalkeeper Dimitry Bertaud.
France were quiet throughout but finally came to life in the final 20 minutes as Scotland retreated into their own half.
Substitute Steve Ambri made an immediate impact and finally forced McCrorie into a save with a towering header which was heading into the top corner but for a stunning one-handed save from the Rangers keeper.
Ambri then had a shot saved at the near post and there were a succession of low balls that just evaded the French strikers as they were frustrated by a compact and deep Scottish defence that did enough to cling on to the lead.
Hibs kid Ryan Porteous lined up in defence for Scotland while Hearts teenager Chris Hamilton came on as a late substitute at right midfield.
The win puts Scotland above their opponents in Group B, and a win over South Korea on Saturday should see them through to the semi-finals.
Scotland: McCrorie, Ralston, Kerr, Porteous, Taylor, Burke, Campbell, Wilson, Johnston, Gilmour, Hornby. Subs: Doohan, Harvie, Burt, Wright, Watt, Middleton, St Calir, Wighton, Hamilton.