Laura The most important question if a key should be real one or just symbolic.
I agree with Ines,giving him the key,while the wife is still in her chastity belt,is way stronger than a symbolic one.Much more meaning,in my opinion.
The symbolic part is more when the man ask the father of the woman the hand of his daughter("la main de sa fille",in french,not sure if it is the same expression in english),which consist a bit in asking her father if he's ok they marry.Not used often presently,but it was very important some times ago,and,if the father said "No.",they woulnd't marry,even if they both wanted to.