Pre-Existing Business

What is the name of your state? Louisiana
Is it illegal to operate a business as a sole proprietorship which includes (husband and wife) with the business under the husbands name (last name only) and the business checking account under wifes name (first & last name)?

What does your city, county licensing authority say? Or have you called the city clerk's office to find out?

The only problem you're going to have is the bank account. Most banks will allow a private individual to have an account under their name for a business but must have a DBA license so while the account will be under your wife's name, there will be a DBA [business name] attached to the file.