Is shoes is a proper noun?

No, the plural noun "shoes" is a common noun, the plural form of the singular noun "shoe", a general Word for a type of covering for the foot; a general Word for something resembling a shoe in form or function; a Word for any shoes of any kind.

A proper noun is the name or title of a specific person, place, or thing; for example, Shoes 'n' More in Greenwich, CT or "The Shoes of the Fisherman" a novel by Morris West.

The Word "shoes" is also the third person, singular of the verb to shoe.