The original question was which "based" airline in this region operated Caravelles, to which the answer I would give would be AirCalin, 1983-87, running from Noumea to Australia and New Zealand. The English-language Wikipedia AirCalin page is only a summary, not covering the Caravelle, but the French version is much more descriptive.
http://fr.wikipedia.org/wiki/Aircalin
However, well before this UTA did have Caravelle operations out of Noumea as well, and in fact on the same routes. UTA, a French long-haul airline from Paris, had a range of bizarre operations, but their Caravelle were one of the most extraordinary. They only bought two, in the mid-1960s. One ran from Paris two or three times a week, hip-hopping through some African minor points, which lacked the airfield facilities and/or loads to warrant a mainstream DC-8. The other was based in Noumea and ran services around the Pacific, again on very low frequency; it had taken over from a DC-4 which did the same thing. Quite how UTA managed to operate efficiently just two Caravelles, each based at opposite ends of the earth, has to be one of those mysteries, just like how they managed Los Angeles to Tahiti near-daily for many years when their only licences connecting this with their Paris base were out through Asia and across the South Pacific - and they did send their DC-8s, and later DC-10s, this way, running Paris-Asian points-Noumea-Tahiti-LAX, then doing one or more LAX-Tahiti shuttles, as well as Tahiti to Tokyo and Sydney, finally picking up a return leg to Paris. French flight crews were on a (doubtless very pleasant) long-term secondment to Tahiti or Noumea, but all the maintenance beyond daily line checks was done in Paris. I do wonder if there were any AirCalin Caravelle captains in Noumea who had, 20 years before, been junior UTA Caravelle first officers there.
Here's part of the 1968 UTA schedule in the Pacific, complete with the Caravelles
http://www.timetableimages.com/ttima...68/ut68-06.jpg
Now while I am writing this, I recall there was also for many years a detachment of French Air Force Caravelles in Tahiti as well, supporting the French missile tests in the area. Here's two of them.
http://www.airliners.net/photo/Franc...0be9e4c80edaab