From what I've seen of Pope Francis, I'd imagine it would be wide open, huggable and smiles all the way around. Yes he is the Pope and there's always been kind of a protocol as far as meeting him but he's just a likable kind of guy it seems. My mother did have a chance to meet Pope John Paul II and she was just awestruck by the aura of peace the man had.
But anyways, back to the subject at hand, there are just traditions whether it be in a church or with royalty or in many different situations where certain things are done to show respect, reverence, humility and such. In times past even servitude and obeisance. Times have changed so much these days that what suits one person/culture may seem strange to another. My mother for example would die before she wore a pair of slacks to church in the 50s-60s. As times changed, so did she.