Say, that’s a dang cool map. I like the “Baye de Baffin”. No Northwest Passage to be seen. And what the heck is that off the west coast of BC? Ohhh, wait a minute. I think they have Alaska as an archipelago, with a pretty substantial chunk of the Pacific between it and the rest of NA. Wonder how they thought there was ocean there. No Vancouver Island to be seen. That seems odd to me. I thought the British already had a colony there by 1780, though I guess they probably didn’t share their cartography with the French, and the French navy wasn’t in the habit of making long voyages, what with being constantly blockaded in their ports by British 74’s and all.
The same way we do now, by surveying. People were already surveying by the early 1700s (?) or so. If you look closely at the map the shipping lanes are very well defined while the rest, Greenland and Australia, look pretty bad. The shipping lanes are the most important, at least on a map like that, which really wouldn’t be used for much more then finding distances and the shortest distances between points. That and once you’ve got one map at a larger scale it’s a lot easier to make smaller scale maps like that one.