We put this question to Shaykh ‘Abd-Allaah ibn Jibreen (may Allaah preserve him), who answered as follows:
It is not permissible for him to go to the church, because this implies respecting and venerating it, and exposes him to developing a liking for Shirk and its followers. He has to break this promise and explain this ruling to the kaafir so that he will understand why the Muslim broke his promise. And Allaah knows best.