how does father madeleine act when he becomes mayor

I'm not sure what you mean. The King appointed him mayor twice, and he refused twice. It wasn't until after the townspeople urdeg him on that he finally accepted.

From the text:

"In 1820, five years after his arrival in M. sur M., the services which he had rendered to the district were so dazzling, the opinion of the whole country round about was so unanimous, that the King again appointed him mayor of the town. He again declined; but the prefect resisted his refusal, all the notabilities of the place came to implore him, the people in the street besought him; the urging was so vigorous that he ended by accepting. It was noticed that the thing which seemed chiefly to bring him to a decision was the almost irritated apostrophe addressed to him by an old woman of the people, who called to him from her threshold, in an angry way: ‘A good mayor is a useful thing. Is he drawing back before the good which he can do?’