... are so called because they were originally made to enable huntsmen to take their watches with them on their horses (themselves known as hunters) and take them out of their pockets to tell the time.
They are also known (not only in France, apparently) as savonnettes – because the cover gives them a shape similar to that of a bar of soap (savon being the French word for soap).
A watch whose cover has a glass panel, so that you can tell the time without opening it, is known as a half hunter or demi–savonnette.
© Haydn Thompson 2020