I have a client that paid expenses out of the plan to pay for expenses for financial accounting information pursuant to SFAS No. 106. It is my understanding that this is a fee that is not allowed to be deducted from a Plan. What would be the correct way to make the correction to the plan?

FAS 106 (or SFAS 106) deals with how to report a liability on a financial statement for postretirement benefits which are NONPENSION related. Generally, this accrued liability is a reflection of retiree medical benefits provided by a company plan.
I agree that no expense should have been charged to the plan, unless it was charged against the employers postretirement health plan under IRC 401(h).

Employer must pay the money back to the retirement plan.

Is that good enough or do they need to do VFC as well?

It depends upon the amount involved compared to total plan assets. If it constituted more than 5% of the plan's assets, I would say to go through the fiduciary correction program since it becomes a reportable event on the 5500.