This is another set of words that I see misused often. In news media, magazines, and yes, even in print. Your editor really is your best friend!
Instead of explaining the ridiculous English rules, I try to find ways to help you, and me, remember how to use these words correctly. They are not interchangeable.
Accept means you allow something; you agree; you take it as it is.
Except means “only if”; it is a type of condition you set upon someone or something.
I accept your proposal. I cannot accept this gift.
(If you said “I cannot except this gift”, it would make no sense).
You can either accept, or not accept, something.
I agree, except for the part where I do not get paid.
Everything looks good, except for your references.
Most of this looks good, but there is an exception. There is a part I do not agree with.
Accept means to agree (mostly), and except means you agree, but for one part.
Unfortunately, they both seem to be interchangeable. The best way I remember is accept means yes, and except means no. It will not work in every situation, but it will work in most.