About this route:
A direct, nonstop flight between Chatham Islands (CHT), Waitangi, Chatham Islands, New Zealand and Le Puy - Loudes Airport (LPY), Le Puy-en-Velay / Loudes, Haute-Loire, France would travel a Great Circle distance of 12,348 miles (or 19,873 kilometers).
A Great Circle is the shortest distance between 2 points on a sphere. Because most world maps are flat (but the Earth is round), the route of the shortest distance between 2 points on the Earth will often appear curved when viewed on a flat map, especially for long distances. If you were to simply draw a straight line on a flat map and measure a very long distance, it would likely be much further than if you were to lay a string between those two points on a globe. Because of the large distance between Chatham Islands and Le Puy - Loudes Airport, the route shown on this map most likely appears curved because of this reason.
Try it at home! Get a globe and tightly lay a string between Chatham Islands and Le Puy - Loudes Airport. You'll see that it will travel the same route of the red line on this map!
The distance between CHT and LPY makes them almost exactly antipodal (the exact opposite side of the world) to each other. Nonstop flights between Chatham Islands and Le Puy - Loudes Airport would be very impractical for the airlines, because only a lightly loaded Boeing 777-200LR would be able to make the trip. Since airlines need to be able to take as many people and cargo as possible in order to make a profit, the odds of ever seeing a nonstop flight between CHT and LPY are slim to none. However, you'll still be able to get from Waitangi, Chatham Islands, New Zealand and Le Puy-en-Velay / Loudes, Haute-Loire, France by taking some connecting flights!
Did you know that one full circling of the Earth (measuring from the equator) is about 24,901.5 miles (or 40,075 kilometers), which means if you were 12,450 miles from any given point on the planet, the distance back to your starting point would be about the same -- in any direction! The same can be said for a nonstop flight between CHT and LPY!