New Zealand's Ofa Tu'ungafasi insisted he never intended to hurt Remy Grosso in a tackle that left the France wing with a double facial fracture.
Grosso, who scored France's only try, came off in the second half following a tackle by Sam Cane and Tu'ungafasi.
Cane's arm appeared to make contact with the head of Grosso, who was then hit in the face by Tu'ungafasi's shoulder as he went to the ground.
France coach Jacques Brunel described the tackle as "illegal", with the French Rugby Federation later confirming Grosso had fractured his face in two places and would play no further part in the tour.
Posting on Twitter, Tu'ungafasi wrote: "Remy, I hope you're recovering well. It was a physical game and it wasn't my intention to hurt you.
"I'm also gutted that I didn't get to see u after the game and u weren't well for me to visit u in hospital this morning [Sunday] before we left but I hope to catch up soon brother."
New Zealand won the first Test at Eden Park 52-11, though France had led 11-8 at the break, the game turning on Paul Gabrillagues' controversial yellow card.