I thought "film" is a noun. But is it used as a verb here?
You are correct that "film" can be used as a noun. however, like most words in the English language, it has multiple usages. One of the usage of the word "film" is as a verb. When it is used as a verb it means to record moving pictures with a camera, usually to make a film for television or the cinema. Ex: Most of the scenes were filmed in a studio. Ex: They filmed for a week in Spain. Ex: We start filming next month. Ex: We've been filming for over 3 months now.