England ground out the required victory to take them to a semi-final encounter against the Kiwis at Wembley on Saturday.
Steve McNamara’s side only added two second half tries but defended for long periods against a French side who were unable to unlock their defence.
England’s first try of the second half came from Sean O’Loughlin, a Rangi Chase kick to the corner was knocked back by Ryan Hall for Leroy Cudjoe’s pass to send O’Loughlin over.
Sam Tomkins, named man of the match, was sin-binned for a professional foul in the closing minutes as England crossed for a late try from substitute Brett Ferres.
Skipper Kevin Sinfield converted all but one of England’s six tries.
See Monday’s League Express for a full report and match reaction.