Yes, but the pronunciation of initial H in words which came into English via French has never been consistent. Initial H of any Latin word would originally have been pronounced. French dropped it, but if it came into English when Latin was still commonly known among the literate, Latin might have been used as a model even if the word came via French, & the H pronounced.
There are some words which came into English from French which are derived from old Germanic words, where the French silent H was pronounced in the original, & has always been pronounced in related English words.
We could either drop the H from all words we got via French where the H was silent when we got it, or pronounce it in all cases where it was originally, i.e. every one. I prefer the latter. It requires much less modification of the language, as there are far more words where we reintroduced the H long before anyone now alive can remember than there are where it was silent within living memory.
BTW, hostage is a word where English added an H which was not in the original. If we're going to insist on original pronunciation we should drop it.
