Melbourne's Webster and Penrith's Pritchard were concussed during a tough but entertaining encounter which the French led 22-20 with nine minutes to go - before three late Kiwi tries gave them a 38-22 victory.
New Zealand must rely on Australia to beat Great Britain in Hull on Sunday if they are to extend their stay in Europe by qualifying for next Sunday's Tri-Nations final and coach Brian
McClennan said he was unsure if the dazed duo would be fit.
"Two head injuries - they've gone to hospital and we'll wait and see," the coach said. "Hopefully, they should be OK."
After battling gamely before losing 44-12 to Australia last week, John Monie's Frenchmen led 6-0 and 12-6 during the first half before the Kiwis snatched a 16-12 advantage at the break.
Cheered on by a vocal crowd in the second half, Les Chanticleers turned on some dazzling footy with winger Olivier Charles dashing over in the corner to tie the game in the 53rd minute.
One Kiwi try later, a Maxime Greseque 40-20 laid the foundation for second rower Sebastien Raguin's second try and a two point lead.
But holding on was too much for the largely part-time French and replacement Louis Anderson (72 minutes), halfback Stacey Jones (73) and fullback Brent Webb (78) silenced the crowd with comparatively soft late touchdowns.
The Kiwi camp was upset with British referee Karl Kirkpatrick, coach Brian McClennan saying: "We would have been lucky to have 25 per cent of the ball in the first half, into the third quarter.
"What am I allowed to say about referees? I'll say: I've seen better."
When it was put to him that the French were passionate, McClennan said: "They were - and good on them. If I had 75 per cent of the ball, I'd be passionate too."
Jones - who returns to Auckland on Sunday for the birth of his third child - said nerves about the Australia-Britain result were such that 'it's like preparing for a game'.
New Zealand: 38 Tries: Iafeta Palea'aesina, David Kidwell, Shontayne Hape, Ali Lauiti'iti, Louis Anderson, Stacey Jones, Brent Webb. Goals: Jones (4), Motu Tony.
France 22 Tries: Sebastian Raguin (2), David Ferriol, Olivier Charles. Goals: Laurent Frayffinous (3).