Is the Capital in the Country?

During a recent conversation, a French person expressed confusion about Washington D.C. and Washington state. Another French person piped in and asked if Washington D.C. was really in the US because it wasn’t a state and wasn’t in a state. I hope she was joking, but after the experience I had with someone thinking that Alaska was an island, I may need to carry a map of the US ready to show to the US-geography-challenged.