Kadeisha Buchanan netted the winner on the brink of half-time in Montpellier to extend the Reds' unbeaten run in 2019 and secure the ideal start to their tournament.
Beckie, making her 57th appearance for her country, completed the full game, starting on the left-wing and proving her side’s main attacking threat throughout.
The 2015 tournament hosts threatened from the off with the 24-year-old delivering three dangerous set-pieces into the box inside the opening five minutes, aimed towards all-time top goalscorer Christine Sinclair – but to no avail.
Beckie herself went close to opening the scoring on 13 minutes with a snap-shot from 25 yards, which flew just wide.
A stop-start period interrupted the flow of the game but Canada – 2015 World Cup quarter-finalists and 2016 Olympic bronze medalists – regained control before the break.
Nichelle Prince saw a deflected effort strike the post in what looked to be the last real action of the half, but another teasing Beckie delivery bore fruit as Buchanan headed home the driven corner at the far post.
With the lead, Canada rarely looked like relinquishing it but the second half would herald few chances for either side.
Beckie – looking to net her 26th senior international goal – curled straight at Annette Ngo Ndom just after the restart, while Claudine Meffometou Tcheno spurned Cameroon's best chance to level with 20 minutes remaining, unfortunate to head just the wrong side of the post.
As Canada looked to seal the win in the dying embers, Beckie skewed wide before drilling once more at Ngo Ndom, and Sinclair was denied her 182nd senior goal thanks to Meffometou Tcheno’s last-minute goalline clearance.
One goal would prove enough for Kenneth Heiner-Møller’s side though, as the Reds hung on for three points.
Canada face New Zealand next on Saturday evening (8pm BST). The Football Ferns lock horns with the Netherlands in their Group E opener on Tuesday at 2pm BST.