To get past this error message, you'll need to clear out all of your mail on that character.
You do not have to worry about deleting mail for the Founder's Pack. That does not count against the character and is accessible by other characters on that Region (NA or EU).
If you still get this message after removing all of the mail from your character's Inbox, check for any outstanding Crafting / Gathering orders from your character. You will need to cancel or retrieve this order before you can delete that character.