Hi,
Just in case.
There was a LE BERTHON family in Martinique whose ancestor is Jean LEBERTHON DE LA RENERIE (and other spellings) born in 1750 in Rouillac (Dordogne, France). He passed away in 1816 in Martinique in La Trinité. He got married to Marie Louise SEVESTRE before 1785. They got at least three daughters. I don't know if there was a son.