If Julie did not name her sons father on any surviving record (birth cert, which you have, or parish register of christening for example) then you will never know who his father was!
Henry may or may not have been. If he was, then one wonders why he took 7 years to marry his mother (unless either party was already married?), so my guess would be he wasnt. But no more than a guess! William may have looked on him as a father, and may name his as such on things like his own marriage cert.
But in cases of illegitimacy, more often than not you just have to accept that you will never know who the father was, and any "guesses" are no more than that, just guesses.
