He already knew or should have known that the weather was below the alternate minima when he got the 0800 SPECI.
At 0756, the captain requested the latest METAR for Norfolk Island from the Nadi IFISO. At 0801, the IFISO provided the 0630 METAR, and at 0802 he provided the 0800 SPECI. Whereas the 0630 METAR was broadly consistent with the current TAF (issued at 0437), the 0800 SPECI indicated the cloud had deteriorated to be overcast at 1,100 ft. These cloud conditions were below the published alternate minima for planning a flight to Norfolk Island, but it was above the landing minima.
He wasn't in the habit of talking about fuel with the F/O so I can only assume he ignored the alternate minima and continued on because he thought that they would get in off the approach. I doubt the issues with the French authorities were even a consideration.