In the phrase thys ys the siege of the hawte prynce from Le Morte D Arthur what does hawte mean?

In normal English this would be something like:

This is the seat of the High Prince

hawte is connected with the French Word haut(high), and means something along the lines of noble / exalted / aristocratic - but it doesn't exactly mean any of those things.

In the Morte D'Arthur Malory is deliberately telling a tale which is old fashioned and fantastical (the Morte D'Arthur was just as old-tyme for people in 1485 as Clint Eastwood's Unforgiven is for us today). Part of the fun is that a few Words don't exactly mean anything at all (though we can say what they sort-of mean).