You can, but it is not common to express the sentence that way. "We are having an English class now" is far more natural.

Normally we would just say We’re in English class. We’re in English. (Both of these work if the people knew what you are referring to) We’re in an English class. (If they didn’t) “Having a class” sounds unnatural from the point of view of a student attending the class. You could say The school has classes in the evening. (The school offers classes in the evening. )