What is the city where king Louis xvi and his family were inprisoned?

Answer 1

Paris, clearly. Where else would they have been imprisoned?

If you mean where were they captured after their ill-fated attempt to flee to Austria (June 20, 1791), that would be Varennes, which is almost on the Austrian border. Most of the key events of the Revolution happened in Paris, because that's where Louis transported his court in yet another ill-advised move after the October 5, 1789, people's (sometimes just called the women's) march on Versailles.