While visiting Pompeii, I was shown the greeting 'HAVE' set into the floor of the 'Casa del Fauno', instead of the standard Latin 'AVE'.
Then there was the picture of the ship in the 'Casa della Nave Europa', which has, written within the frame, 'HUROPA'.
Is this use of 'H' an earlier language (Oscan?), influenced by Latin, or is it a later form of Latin?
Can anyone tell me what it was?

Not sure about Oscan, but "HAVE" is just the archaic (probably pre-Cicero) way or writing "AVE". By the time of that Pompeii mosaic, it should have lost the initial aspiration even though the old spelling was kept.

Could be, but there's also another possibility. Because initial H had gone mute by then, many people didn't know when to write it and when not. In other words, just a misspelling.