Can a storefront loan company demand the interest amount if principal is paid off?

Wait until they validate the debt. Don't pay a penny before that. What is the name of the storefront company? See, legal storefront companies can sue you for payday loan debts.But, much depends on how much you owe. If you don't owe a big amount, then they are less likely to sue you.

Which state are you in? Storefront loans are illegal in few states. If it is illegal in your state, you are supposed to pay only the principal amount.

Ask them to validate the debt, if they can't validate it, they are ilegal lenders,

Have they validated the debt? If yes, then try to settle with the debt collectors. I guess that will be a good option as you have already paid off the principal amount.
If not, then you might not owe the debt. So, you don't need to pay it off unless they validate the debt.
Secondly, find out the statute of limitations (SOL) in your state. If your debts have crossed the SOL, you are not legally bound to pay off anything.
Thirdly, check whether or not storefront loans or that particular lender is legal in your state. If not, you don't have to pay off any interest amount (as you have already paid off the principal amount).