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Kyle Good put the Irish ahead in the first minute but the French hit back with goals from Jean-Laurent Keiffer and Gaspard Baumgarten.
Peter Caruth equalised with a rebound finish and Jonathan Bruton's shot sneaked across the line to make it 3-2 before Shane O'Donoghue added a fourth.
Simon Brisac Martin pulled one back but Ireland held on for the points.
Good gave Ireland the perfect start in the Pool B encounter at Queen Elizabeth Olympic Park, netting just seconds into the game.
Irish keeper Davy Harte made a good save to deny Martin before Keiffer redirected a powerful shot into the net four minutes before half-time.
France moved in front within seconds of the restart with Baumgarten firing high past Harte.
Caruth followed up his shot to convert the rebound while goalline technology was required to confirm Bruton had indeed scored Ireland's third goal.
Martin set up a tense finale and France pressed for the leveller but Ireland held firm to secure a winning start.
Ireland, who need to win the tournament to ensure a place at the Rio Olympics, are back in Pool B action on Sunday against Germany.
"It was a good win and we played well in phases," said Ireland coach Craig Fulton.
"France are a very attacking team and scored some good goals. The result was important for us but we need to improve in every game and we're keen to do that."
Ireland clinched a 4-3 victory over France in their opening game at the EuroHockey Championships in London.