Wiktionary says fromage comes from Latin for "mould", cheese might come from Proto-Indo European "to ferment, become sour" but this is contested, and ost comes from Proto-Indo European "sap"/"juice"/"broth", seen also in Latin ius="gravy"/"broth"/"soup"/"sauce".

See e.g. https://en.m.wiktionary.org/wiki/cheese

Interestingly, the pronounciation guide for origin of ost is /ˈjus.tɑz/ which seems a lot like the Finnish word for cheese, "juusto".