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You are correct. Chabarthes is a somewhat common name in the vicinity of Caunes -Minervois, a town in the high Pyrenées, near Carcassonne. "ainé" (with accent) translates into "the oldest", e.g of two brothers.
In other words, you have a razor made by one Chabarthes sr., from the town Caunes.
There is one reference on the internet of a widow from a Chabartes in the Caunes -Minervois area, who worked as a knife maker. The reference dates back to 1801.