redirect from old cfm website

Hi
I just redid someone’s website from an old cfm website to Shop Theme responsive.
The old website was http://www.theirdomain.com/index.cfm the new website is http://www.theirdomain.com

Although it redirects when someone uses the old home page address (index.cfm) — to a 404 error and the message “This is somewhat embarrassing, isn’t it? It seems we can’t find what you’re looking for. Perhaps searching can help.” I am wondering if I should be creating a file named index.cfm and then put a permanent redirect in it, so that people end up on home page instead of at an error message

Please advise.
Thanks so much