Albus Dumbledore and Hector did not linger any longer. Although Hector showed a very strong interest in wandering around France, Dumbledore refused his suggestion on the grounds of being busy with official business.
Dumbledore took Hector to the French Ministry of Magic to apply for a Portkey back. Since they had arrived informally, they still needed to use legal channels for the return trip; otherwise, it would carry a certain implication of defying the law. What kind of person was Albus Dumbledore? Naturally, he would not leave such ammunition for others to use against him.
Therefore, the moment they returned to France, Dumbledore and Hector immediately headed toward the French Ministry of Magic.
Chapter 86