About 8 years ago, I was offered a car pretty much like that.. White, cherry.. low mileage, old widow, etc. It may have been a Mark VIII.. I forget the details. Her friend said she expected ~$2,000. My T-bird was running fine so I passed it up.
My suggestion is get more details (the year?) and ask your insurance company how much they will pay if it gets totaled, and not pay more than that for it.
Nice car.. parts are a bit difficult to find these days, but with a little luck it should provide fine basic transportation for many years.