When I hear the word cordial, I think of somebody who is trying to remain polite to somebody he doesn't particularly like. I think it is because I've often read sentences like, "o.k., let's try to remain cordial."

The way I sign off depends upon who I am writing to.

For friends, French or English, I typically write Salut ("bye" in French).

Business correspondence varies. I use "regards" most often. If it is a harse e-mail or letter, I don't use a sign off. Why say regards, when I don't mean them. In French correspondence, the whole, "please accept our sincerest..." type of closing is still in use here and the variety is large depending on who you are writing.