Edit: it looks like you are asking about the French colony of New Caledonia. If so none of the titles I listed will be of any use to you. New Caledonia was also the name given to a fur trading region in the heart of British Columbia in 1806. It was recommended as the name for the new British colony created in Western Canada in 1858. This name was rejected by Queen Victoria who picked British Columbia as the name in order to prevent confusion.

George and Helen Akrigg wrote the "British Columbia Chronicles" Volumes I and II that contain many first hand accounts of the history of the province and the interior.

Gordon Bowes published the "Peace River Chronicles" which is mostly concerned with the Peace River Country but includes a good deal of information about the fur traders and gold miners who lived and traveled in the Peace River, Omenica and New Caledonia.

Ann Bancroft's "The History of British Columbia" has long been considered to be one of the best history books on the subject.

Father A. G. Morris was a Catholic priest living in the region in the late 1800's. His book "The History of the Interior of British Columbia" includes the oral history of the Carrier Indians from around Fort St James as told to him by K'wah, the principal chief of that region

"The Land of Twelve Foot Davis" by J. G. McGregor details the life and times of one of the most famous traders and miners who traveled back and forth between Quesnel and Peace River, Alberta.

"Daniel Harmon's Journal" was written by a Northwest Company fur trader who lived at Fort St James from around 1811-1821. His journal contains many first hand observations of the Carrier Indians he lived among just 5 years after the Europeans first made contact with them.

The Hudson's Bay Records Society published Simon Fraser's Journal covering his explorations from 1806-1808 and Samuel Black's journal covering his 1821 explorations of the Finlay, Sustut and Turnagain rivers. The Records Society also published many volumes of outgoing and incoming letters including those from New Caledonia from the 1820's to about the 1870's.

There are many books about Sir George Simpson, the Governor in charge of all of the Hudson's Bay Company's North American interests. Archibald MacDonald published his journal he wrote when he accompanied Simpson during 1821 canoe trip from the Hudson's Bay to Fort Vancouver in Oregon. "The Fur Trade Governor" is an excellent book that covers Simpson life and work in North America, and Simpson's own journal he wrote as he traveled around the world by land across North America and Russia in 1841 is also a fascinating read.

Henry Dunn, Peter Skene Ogden, John Connolly, A. C. Anderson, Sir James Douglas were Northwest Company and Hudson's Bay Company traders who all kept journals that have been reprinted via the Guggenheim project. These books are available today and much, much more affordable than the first editions that kept me broke when I started to get the buying them ten years ago.

If you look through my posting history in this sub you might find some other titles of interest to you. The history of British Columbia and western Canada is my passion and has become a very deep rabbit hole with many tweets and turns for me.