The Irish had to dig deep to deny France an equaliser, with goalkeeper Jaime Carr making several world-class saves to secure the victory for his side.
With both sides already qualified, Ireland were seeking a fifth successive victory in Santiago, Chile.
They produced the best opportunity of the early stages as a crash ball across the circle gave Louis Rowe a chance to deflect towards goal, but it hit his back stick and the game remained level.
The second quarter began superbly, when Jeremy Duncan and Sean Murray connected well with Duncan having a strike on goal which was well saved.
France responded well, building some phases in Irish territory and eventually working an opportunity to shoot in the circle, but Alistair Empey made a good block to deflect the ball high and wide.
Ireland’s Jamie Carr with his Player of the Match award. Photo: Javier Torres/WORLDSPORTPICS
Their opponents won the first penalty corner of the tie for a foot in the circle. They opted for a variation, working the ball back across goal where Louis Haertelmeyer touched it into the net.
Then came the fightback, with Feargus Gibson doing well to break into the circle and find a foot to win a penalty corner.
Williams then rifled the ball into the net for his second of the tournament to draw Ireland level going into the break.
The intensity of the tie continued into the second half, as France immediately tried to restore their lead, but Carr kicked clear.
It wasn’t long before the Corinthian player fired into the French net for his second.
France though immediately went in search of an equaliser, with Carr called into action, followed by a second chance that went just wide of the far post.
Carr made a huge double-save in the closing minute of the third quarter to maintain Ireland’s lead.
The French pressure carried into the final quarter, with Kyle Marshall required early on to make a last-ditch block.
Ireland, however, remained positive in attack looking unsatisfied with their two goals, but individual errors in the final third denied them chances at goal.
France withdrew their keeper with two and a half minutes remaining. A penalty corner with just over ninety seconds remaining gave them one last chance, but once again Carr stepped up to deny them with a superb stick save.
Ireland’s win sees them secure top spot with a perfect record in the FIH World Cup Qualifiers and will also see the side lock down ninth in the World Rankings.
The team will turn their attention to the FIH Hockey Nations Cup this summer before the all-important FIH Hockey World Cup in August.