Is they a proper noun or a common noun?

They is not a proper noun or a common noun. The Word 'they' is a pronoun, a Word that takes the place of a plural or multiple nouns; the third person, subjective form. The pronoun 'they' can take the place of common or proper nouns; for example:

The dogs have had their walk, now they want food.

Fran and Frank are coming to lunch; they will be here at one.