French cannot be the "original language" because Hix exists before French became in use at Hix. In Pyrénées-Orientales (but Fenouillèdes), the "original language" is catalan. Even in late 19th century only "educated" people spoke French, which is the only official language, is become the main language but is not any "original language". Please, could you read some sources about Hix and Pyrénées-Orientales? For example, have a look at French official Geoportail https://www.geoportail.gouv.fr/carte , search for Hix and you'll find "Forques Llargues", "Campori", Càldegues, etc just next door, all catalan names (the books read the same). Bourg-Madame is different: there is an official name because it is a commune (and an "original language" name in French, for once, because this name was created from scratch during the 19th s).
In short for Pyrénées-Orientales "original language"=Catalan", "official name"=French (when there is any offical name). We shouldn't revert without any reading any source before.