Start by naming any country that France borders. Then name any country that borders any of those countries. Then keep going until there are no more countries left to name.
It's a little funny that you wanted to prevent spamming two-letter combos so you only accepted states/elements, but then you still gave us 6 minutes. It took me about a minute to just guess every state, and while I'm a relatively fast typist, I can guarantee the majority of people on this site can do the same in the given time, and probably much less. I might consider decreasing the time.
I don't know what answers you put in the quiz, but they're wrong.